Okay. well. Prime factorization can be used to find a lot of things, I'm assuming. However, the primary purposes in our class is just finding the least common multiple (LCM) and the greatest common divisor (GCD). FOR EXAMPLE, if you were given two numbers and told to find the LCM, you would just find the prime factorization and multiply every number (highest degree between both). Easy enough right? Well, GCD is just multiply all the numbers they have in common to the lowest degree. Also, prime factorization can be used in practical situations when like trying to find how many prime numbers of marbles can I put in a cup...etc.
This prime factorization is related to crytography in that, most likely, different variations of prime numbers/factorization will be used when categorizing each letter.
OKAY..so I'm done. kthnxbye.
Sunday, October 31, 2010
ahhh
Prime factorization can be used to find number of diviors, what the divisors are, divisors that are multiples of 2 or square root of 3 or perfect squares and all that good stuff. you can use it to simplify fractions by breaking down the number on top and the one on bottom.
question 2 .
okay, we are taking number theory/cryptography right? and what are we learing in this class i speak of, oh, that's right, prime factorization, so they obviously have something to do with each other, haha.
and do these blogs have to be 150 words too? becuase i remeber on previous blog prompts that they didn't require long answers.
question 2 .
okay, we are taking number theory/cryptography right? and what are we learing in this class i speak of, oh, that's right, prime factorization, so they obviously have something to do with each other, haha.
and do these blogs have to be 150 words too? becuase i remeber on previous blog prompts that they didn't require long answers.
Halloween Blog emohgniogm'i,syuguoywercs#
What are the different uses of prime factorization?
Uhh.......finding LCM's and GCD's?
Is it realted to cryptography?
possibly.......if I knew what cryptography was, I'd give you a definite answer though...
Uhh.......finding LCM's and GCD's?
Is it realted to cryptography?
possibly.......if I knew what cryptography was, I'd give you a definite answer though...
halloween post.
Prime factorization can be used to find many things. it's about breaking things down.. going back to the basics.
it's used for things like finding lcm, gcd, ... exponential form, # of divisors, product of divisors... & to simplify fractions, etc.
cryptography is used to break down & decipher codes. prime factorization is used to break down numbers.... sounds similar right? well i'm sure, in some strange way, it is used in cryptography. we'll probably learn how to do that in the 2nd semester.
it's used for things like finding lcm, gcd, ... exponential form, # of divisors, product of divisors... & to simplify fractions, etc.
cryptography is used to break down & decipher codes. prime factorization is used to break down numbers.... sounds similar right? well i'm sure, in some strange way, it is used in cryptography. we'll probably learn how to do that in the 2nd semester.
Helen's Bloggggg
What are the different uses of prime factorization? Is it realted to cryptography?
In class we use prime factorization to find the gcd, lcm, number of divisors, the product of the divisors, and many others things that I don't know how to do :). I think it is related to cryptography because it might help codes and stuff and it makes the number simpler.
In class we use prime factorization to find the gcd, lcm, number of divisors, the product of the divisors, and many others things that I don't know how to do :). I think it is related to cryptography because it might help codes and stuff and it makes the number simpler.
Chapter 10
This past week, we have started off learning the formulas needed in Chapter 10.In order to find the right answers, you MUST know your trig chart since there is no calculators being used. You also have to know your formulas. You need these when finding the exact value, simplifying the expression, etc.
List:
List:
- Cos(A+/-B)=CosACosB-/+SinASinB
- Sin(A+/-B)=SinASinB+/-CosBCosA
- Tan(A+B)=TanA+TanB/1-TaNATanB
- Tan(A-B)=TanA-TanB/1+TanATanB
Double Angles:
- Sin2A=2SinAcosA
- Cos2A=Cos2A-Sin2A
- Cos2A=Cos2A-1
- Cos2a=1-Sin2A
- Tan2A=2TanA/1-Tan2A
Half Angles:
- Sin2a=+/-(Square root)1-cosA/2
- cos2a=+/-(sqaure root)1+cosA/2
- tan2a=1-cosA/sinA=sinA/1+cosA
We use these formulas to find out these unknown trig functions ex:sin75degrees
Prime Factorizatioin
In Number Theory, We use the prime factorization method for many parts of math.
- Finding the GCM and LCM of sets and numbers
- Finding how many divisors a number has
- To find the product of the divisors of numbers using n^t(n)/2
- Place numbers in expo form
- Find the prime fact.
We used prime factorization because it would be helpful in breaking down large numbers into certain groups easier than some other methods.
I'm certain that Prime Factorization is related in cryptology since cryptology has something to do with breaking and deciphering codes using conventional methods. Prime Factorization is used in other maths to help solve numbers easily in different problems
Halloween Blog of the Dead -topsgolbredrum
What are the different uses of the uses of the uses of prime factorizationings? Oh I'll tell ya. I'll tell ya alright. We use prime factoriaztions for many a thing in B-Rob's 5th hour numbr theory class. We use it simply to use it. We use it simply not to use it. We use it to find the greatest cmmon denominators and least common mulltiples of 2 or more dieffernt numbers. It is a eraly col method of findngig numbers and ish tha is usefull. we also use prime ffactoriazaitonns to find the total number of divisors , perfect swuares and cubes and products of the greatest commmon denominators and least common mulltiples of two or more numbers. you can also simplify fractionss by using the method of prinme factorizations.
Is it realted to cryptographY?
yea i think it is but not in a very applicable way, ya know what im sayin. maybe you gota break down numbes and stuff to find a diffetrnt way to deciperh a code or somehting lkike that. You gotta break down the numbers in a way to try to simplify them into somehthing simpler. that's all i really got right now i can't think of anything else.
10/31/10 CHASE :D
what are the different uses of prime factorization? some uses are for finding LCM, GCD, the number of divisors in a number, the primes a number is divisible by, finding the product of divisors of a number, and putting a number in exponential notation.
is prime factorization used in cryptography? im sure it is. cryptography... as far as i know, is the breakdown of hidden codes through numbers; im sure prime factorization plays its role in some forms of cryptography because it simplifies much more complicated numbers down to its primes, and that could be VERY useful in cracking code
is prime factorization used in cryptography? im sure it is. cryptography... as far as i know, is the breakdown of hidden codes through numbers; im sure prime factorization plays its role in some forms of cryptography because it simplifies much more complicated numbers down to its primes, and that could be VERY useful in cracking code
Kaitlyn's blogggg
What are the different uses of prime factorization? Well in class, we have been using prime factorization for things like finding the gcd, lcm, numbers of divisors, and other very complicated things. Prime factorization make it easier to figure out different problems because it simplifys a number down. I'm pretty sure we will be using prime factorization in crytography. We might use it to help us decode different things because prime factorization simplifys the number down, this would make it easier to do. I'm sure that prime factorization is used in many different types of math and we will be using it all the time now.(:
10/31/10
*Some uses for prime factorization (that we've done in class) are as follows:
-to find the GCD/LCM of a set of numbers
-to find what prime numbers a number is divisible by
-to find the number of divisors a number has
-to find the product of the divisors of a number using the formula n^t(n)/2
-to put a number in exponential notation
-to basically break down very large numbers into work that is easier to decipher
*Is prime factorization related to cryptography?
Yes it sure is. Cryptography is basically the study of secret codes; how to make and break them..As far as I know anyway. And in order to break them, I'm sure you have to know the prime factorization of numbers to make it simpler and easier to understand. Of course if you were dealing with very large numbers, it would take a long time to decode them (or whatever you will have to do..). Using prime factorization just seems like it would make the process quicker and simpler. And I'm sure in cryptography there are many other methods to use besides the prime factorization, such as for instance, Bezout's Theorem and the Euclidean Algorithm...(And no I didn't already know this, I'm not that good, haha. I kinda sorta got this off of our topic list for the class :P)
-to find the GCD/LCM of a set of numbers
-to find what prime numbers a number is divisible by
-to find the number of divisors a number has
-to find the product of the divisors of a number using the formula n^t(n)/2
-to put a number in exponential notation
-to basically break down very large numbers into work that is easier to decipher
*Is prime factorization related to cryptography?
Yes it sure is. Cryptography is basically the study of secret codes; how to make and break them..As far as I know anyway. And in order to break them, I'm sure you have to know the prime factorization of numbers to make it simpler and easier to understand. Of course if you were dealing with very large numbers, it would take a long time to decode them (or whatever you will have to do..). Using prime factorization just seems like it would make the process quicker and simpler. And I'm sure in cryptography there are many other methods to use besides the prime factorization, such as for instance, Bezout's Theorem and the Euclidean Algorithm...(And no I didn't already know this, I'm not that good, haha. I kinda sorta got this off of our topic list for the class :P)
Justin
We use prime factorization for things like GCD, LCM, number of divisors, product of divisors. It makes problems easier because youre shrinking it down into powers of primes. I think we are going to use prime factorization for cryptography, but I don'r really know how.
There are multiple uses of prime factorization, though we have only gone over a few. One way we used prime factorization was to find the least common multiple, greatest common denominator, and finding how many divisors and so forth.
Finding the prime factorization is very helpful becasue it is often easier to work with smaller numbers rather than doing intense math.
I believe that cryptogrophy will use prime factorizations to help decode the problems because you may be able to find a code and be able to realize that the gcd equals one letter than the same for antoehr.
It is very important that we learn to do the prime factorization of numbers because it is used in a varitety of problems.
Finding the prime factorization is very helpful becasue it is often easier to work with smaller numbers rather than doing intense math.
I believe that cryptogrophy will use prime factorizations to help decode the problems because you may be able to find a code and be able to realize that the gcd equals one letter than the same for antoehr.
It is very important that we learn to do the prime factorization of numbers because it is used in a varitety of problems.
Blog Prompt
Jordan's computer is currently down. Thus I will be posting this week's blog prompt.
What are the different uses of prime factorization? Include some we have done in class and some that you find. Also is it related to cryptography?
What are the different uses of prime factorization? Include some we have done in class and some that you find. Also is it related to cryptography?
Wednesday, October 20, 2010
Feroz's Blog
I feel like I've mastered quite a bit in this class, like the sieve, finding the gcd and lcm, and definitely prime factorization.
I struggled with the word problems, like "find the number the divisors of 100,000,000,000 that are perfect squares" and stuff like that. Just not to that extent.
I never really took this class seriously, and I still don't, so I should probably do homework and rework problems to improve my grade.
I struggled with the word problems, like "find the number the divisors of 100,000,000,000 that are perfect squares" and stuff like that. Just not to that extent.
I never really took this class seriously, and I still don't, so I should probably do homework and rework problems to improve my grade.
Sunday, October 17, 2010
DaViD
I've mastered alot in this class. The seive is easy, just takes alot of work and writing numbers. prime factorization is something that is now super easy to understand and work. I can work matrices and logs. I struggled with some of the weird word problems we had in homework, and one way i can fix my grade and fix that is possibly doing that homework more often and to the fullest extent. I will be doing amazing in this class from now on because i want the food prize EVERYTIME we cipher. amen.
Blog for 10/17
What concept do you feel like you mastered this nine weeks?
Hmm, I honestly don't think I've "mastered" any concepts this nine weeks, but I've started to get better with the whole LCM AND GCD thing
What concept did you struggle with the most? Why?
well, I have no clue actually, I'd have to go with finding prime numbers because I'd always forget one little common mistake and get the numbers wrong
What can you change this nine weeks in your study habits, etc to improve your grade?
I'd have to go with doing the homework twice I guess
Hmm, I honestly don't think I've "mastered" any concepts this nine weeks, but I've started to get better with the whole LCM AND GCD thing
What concept did you struggle with the most? Why?
well, I have no clue actually, I'd have to go with finding prime numbers because I'd always forget one little common mistake and get the numbers wrong
What can you change this nine weeks in your study habits, etc to improve your grade?
I'd have to go with doing the homework twice I guess
Muuraaayyy
The concept I mastered is prime factorization. It was easy to begin with, but now I can go really fast and it doesn't take near as long. I get alot of the processes we learned, and I will most likely remember them because they make sense, it easy( well not easy but yea) to figure it out with some thinking. I struggled alot with logs! I will never get them! What i could do to help is perhaps go to alpha practice with shawn... and at first, i had heard that the math extra class was just to focus math club, not this. So i'm ready now. I know my study habits wil change, in fact, they could get reall, because i already focus all homework time on advanced math, so it that class gets harder, i'll really be in trouble, with that one and this one. anyway, this nine weeks was rough, but at least i can find the all the prime factors between 1 and 100. haha,
MalPal
Okay. so the following:
What concept do you feel like you mastered this nine weeks?
Umm..Hello? Prime factorization. It gets intense sometimes, but you don't even have to really think about it, or at least I don't. I just divide and divide and divide till no end. So, to answer the question, I have indeed mastered prime factorization.
What concept did you struggle with the most? Why?
I struggled with the whole let's find all the multiples of whatever under 10000 that are perfect squares. I think I don't get this because I never know like what to put the prime factorization over like what you do with
What can you change this nine weeks in your study habits, etc to improve your grade?
Rework problems
What concept do you feel like you mastered this nine weeks?
Umm..Hello? Prime factorization. It gets intense sometimes, but you don't even have to really think about it, or at least I don't. I just divide and divide and divide till no end. So, to answer the question, I have indeed mastered prime factorization.
What concept did you struggle with the most? Why?
I struggled with the whole let's find all the multiples of whatever under 10000 that are perfect squares. I think I don't get this because I never know like what to put the prime factorization over like what you do with
What can you change this nine weeks in your study habits, etc to improve your grade?
Rework problems
Justin 6
What did i master this 9 weeks? Hehe prime factorization related stuff which includes gcd lcm #of divisors product of divisors and so on. i like this stuff cause i grasp it quickly and work relatively fast with it. what i could do to improve my grade would be to practice more so i'll be more accurate and quick. other than that, i think i did pretty good this 9 weeks
kmart(:
What i feel i've mastered the most this nine weeks is lcm and gcd. This is reallyy easy because all you have to do is find the prime factorization of your number and solve for it. It takes me no time at all to do this, i could probably do it in my sleep. Also with finding the prime numbers between a set of numbers like 1-100. The concept i struggled the most with was when we got more into the prime factorization concept, like finding the divisors and other things like that. It's really confusing for me and i'm not really good at understanding exponents. Other than that, i think i did pretty well this nine weeks.
Helen Melon :)
What I think that I mastered this nine weeks is how to find the gcd and lcm of two or more numbers by using the prime factorizations of the number. I also learned how to find the prime number between 1-100 by using the sieve. What I struggle the most with is finding the multiple divisors, conics, and exponents. What I should do to improve my grades is to pay more attention and study more
Alaina's blog, 17 October 2010
What concept do you feel like you mastered this nine weeks? What concept did you struggle with the most? Why? What can you change this nine weeks in your study habits, etc to improve your grade?
The concepts that we learned this nine weeks reflect on childhood math (elementary math). The GCD and LCM we learned in probably the 4th grade and had to learn again in 10th, 11th, and 12th grades. The concepts are fairly simple, but because we have been doing things much harder for a lot of years, we make them more complicated than they are.
The concept that I struggled with this nine weeks would be the product of all positive divisors of some number n. I can never remember the formula for this; therefore, I spend the majority of my time on tests doing this the long way. And I finally give up on it and move on to simpler problems.
This nine weeks, I could have studied a little bit more for the tests and quizzes in this class. Studying more would have improved my grades. I also procrastinate tremendously! So I need to work on these things.
The concepts that we learned this nine weeks reflect on childhood math (elementary math). The GCD and LCM we learned in probably the 4th grade and had to learn again in 10th, 11th, and 12th grades. The concepts are fairly simple, but because we have been doing things much harder for a lot of years, we make them more complicated than they are.
The concept that I struggled with this nine weeks would be the product of all positive divisors of some number n. I can never remember the formula for this; therefore, I spend the majority of my time on tests doing this the long way. And I finally give up on it and move on to simpler problems.
This nine weeks, I could have studied a little bit more for the tests and quizzes in this class. Studying more would have improved my grades. I also procrastinate tremendously! So I need to work on these things.
10/17/2010
What concept do you feel like you mastered this nine weeks? What concept did you struggle with the most? Why? What can you change this nine weeks in your study habits, etc to improve your grade?
This nine weeks I feel that I have mastered many new concepts that I never thought I would learn or have to learn. The concepts are basically elementary concepts, and I never knew something so complicated could be so simple, and I never knew something so simple could be so complicated.
Anyway, I feel that I definitely mastered the concept of finding prime factorizations for different numbers. Also, I feel totally comfortable with LCM and GCD now, more than ever before in my life, I feel like a pro at it.
The concept I struggled with the most this nine weeks would probably have to be conics, exponents, and finding the exact factors of a number once you find the prime factorization. I've always had trouble with conics, especially parabolas for some reason, exponents are ok, but sometimes they can be complicated, and finding those factors just takes a long time and I get lazy and don't feel like doing them I guess.
What I can change the next nine weeks is definitely just study more and more every night, and stop procrastinating in class and actually try to pay attention to the subject material being taught.
10/17/10
The concept I feel like I've mastered this nine weeks is definitely prime factorization, and using the prime factorization of numbers to find the lcm and gcd. That is extremely easy for me now and I don't even have to think about it. I know exactly what I have to do by simply glancing at the problem. I also feel I've gotten better with recognizing what you have to find in word problems. (For instance, if they're asking for the factors of a number, the gcd, etc.) The concept I struggled with the most I think is in Chapter 5..It has to with the number of divisors a number has, but that's all they give you in a problem and they ask you to find, for example, x^3 if x has 14 divisors. Problems like that still confuse me and I could use more practice with them...To improve my grade I can study more thoroughly the night before and actually rework the problems from the review pages, to make sure I know what I'm doing. Other than that, I think I'm doing okay in the class..it just takes me a little while to catch on to things ha
Recap Post
This nine weeks i felt very comfortable with most of the topics. I especially felt comfortable with the factor trees and GCDs and LCMs. The one thing i was not comfortable with was when to do the t^n/2 formula. That is definately the easiest thing ever and most people are probably laughing at me, but honestly, i never knew when to use it. Another thing i felt comfortable with was the groups of pennies and then how many different ways..that stuff was easy.
This nine weeks went by pretty fast with some pretty easy terms and topics. Hopefully the next three are the same!
This nine weeks went by pretty fast with some pretty easy terms and topics. Hopefully the next three are the same!
Post
I feel like I have mastered how to use the prime factorization to find the gcd and the lcm of two or more numbers. This is a much easier process then trying to compare all of numbers. I still am having problems with when they tell you to find the multiples of some number between two numbers using the prime factorization, so instead I just use the sieve. I think that I can improve my grades by looking over what we did in class and doing my homework every night.
ReCaP
The lesson in number theory that i have i mastered the most is finding the greatest common divisor(GCM) and the least common multiple(LCM) of numbers by using prime factorization. Before NUmber theory, i knew how to find them but it took me alot longer than it should have. I stuggle to find the product of the LCM of a number. I tend to get that confused with finding common divisors. Maybe i should stop kidding around in class and ask more relevant questions pertaining to the lesson.
Saturday, October 16, 2010
postttt.
What I feel like i've mastered this nine weeks is how to find lcm and gcd. i always knew how, but i would get it confused between the two of them. from so much practice, i don't think i will ever forget it now. I struggle with how to find gcd if given the lcm. I don't understand how that's possible. I need to take more legible notes, and maybe I could understand what i was actually writing down.
Thursday, October 14, 2010
4 most important numbers
Hmm For my four most important numbers I would have to go with pi, and e. As far as two others I would go with the golden ratio because of the significance that it holds and i (which is imaginary but still pretty important... I'm not sure if I can count i..) Pi because almost all geometry and trig need an approximation of pi so it is used in tons of applications, and e for a similar reason.
Just thought I would add the thoughts off the top of my head to this one...
Just thought I would add the thoughts off the top of my head to this one...
Blog Prompt
What concept do you feel like you mastered this nine weeks? What concept did you struggle with the most? Why? What can you change this nine weeks in your study habits, etc to improve your grade?
Monday, October 11, 2010
Some comments
I just wanted to note that for the people that got 1/4 for the gcd*lcm problem, you were "correct" in method but incorrect in answer. I meant for the problem to read that a*b = 4096, so it was my fault, but the real problem with the whole thing is that no set of numbers exist satisfying the criteria I gave. I meant for the answer to be 4. Sorry about that.
I'll also comment that I feel like a lot of you (and by a lot of you I mean EVERY LAST ONE OF YOU) were VERY close-minded and didn't give any thought to the most important numbers in mathematics at ALL.
I assure you that there are FAR more important numbers out there than 4, 5, 100, etc. You guys REALLY should strive to think outside of the box sometimes. It won't hurt you and you might learn a thing or two really.
I'll also comment that I feel like a lot of you (and by a lot of you I mean EVERY LAST ONE OF YOU) were VERY close-minded and didn't give any thought to the most important numbers in mathematics at ALL.
I assure you that there are FAR more important numbers out there than 4, 5, 100, etc. You guys REALLY should strive to think outside of the box sometimes. It won't hurt you and you might learn a thing or two really.
Sunday, October 10, 2010
alaina's blog, 10 oct. 2010
Set 1 abstract
question 1: what is the relationship between the gcd and the lcm of two positive integers, a and b?
-the gcd and lcm have common multiples and, usually, the lcm and be divided by the gcd.
for example: (40, 24)
the prime factorization of 40= 2^3(5)
the prime factorization of 24= 2^3(3)
the lcm of 40 and 24 is 120
the gcd of 40 and 24 is 8
question 2: if you were asked to state what you think to be the four most important numbers of all mathematics. i'm not asking for your luck number, or 42, or 1337, or any other quirky/"clever" response. i want to know, mathematically speaking, what you think the four most important numbers are. justify your answer.
-i really do think the four most important numbers are 1,2,3, and 4 because ,first, these are the first numbers one learns as a child. second, when added in any combination, these numbers can form all other numbers 5-10. all numbers 1-10 are the basis for all other numbers, 11-infinity.
Set 2 combination:
question 1: what is the gcd and lcm of the numbers 36 and 84? what is the product of 36 and 84?
-3squared(2squared)=36; 2squared(3)(7)=84.
the gcd of 36 and 84 is 12
the lcm of 36 and 84 is 252
the product of 36 and 84 is 3024
question 2: if the product of two numbers, a and b, is 1024 and the lcm is 4096, what must their gcd be?
their greatest common divisor is 1024.
question 1: what is the relationship between the gcd and the lcm of two positive integers, a and b?
-the gcd and lcm have common multiples and, usually, the lcm and be divided by the gcd.
for example: (40, 24)
the prime factorization of 40= 2^3(5)
the prime factorization of 24= 2^3(3)
the lcm of 40 and 24 is 120
the gcd of 40 and 24 is 8
question 2: if you were asked to state what you think to be the four most important numbers of all mathematics. i'm not asking for your luck number, or 42, or 1337, or any other quirky/"clever" response. i want to know, mathematically speaking, what you think the four most important numbers are. justify your answer.
-i really do think the four most important numbers are 1,2,3, and 4 because ,first, these are the first numbers one learns as a child. second, when added in any combination, these numbers can form all other numbers 5-10. all numbers 1-10 are the basis for all other numbers, 11-infinity.
Set 2 combination:
question 1: what is the gcd and lcm of the numbers 36 and 84? what is the product of 36 and 84?
-3squared(2squared)=36; 2squared(3)(7)=84.
the gcd of 36 and 84 is 12
the lcm of 36 and 84 is 252
the product of 36 and 84 is 3024
question 2: if the product of two numbers, a and b, is 1024 and the lcm is 4096, what must their gcd be?
their greatest common divisor is 1024.
10/10/10 Post (Binary FTW)
Set 1, abstract:
Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?
hmmm, I honestly have no clue at all
Question 2.) If you were asked to state what you think to be the four most important numbers to all of mathematics. I'm not asking for your lucky number, or 42, or 1337, or any other quirky/"clever" response. I want to know, mathematically speaking, what you think the four most important numbers are. P.S., the answer is not 1,2,3, and 4. (Also, there are no right or wrong answers, and if you REALLY think it's 1,2,3,4, just justify your answer VERY well.)
Justify briefly.
well, I'd have to say 0, 10, 100, and 1000 are probably the most important numbers in my opinion
just think about it, multiply anything times 0 and you get 0, or add anything to 0 and the sum doesn't change from the original number
as for 10, 100, and 1000, they create the easiest numbers to multiply and divide by, simple as that, as well as in addition and subtraction
Set 2, concrete:
Question 1.) What is the lcm and gcd of the numbers 36 and 84? What is the product of 36 and 84?
lcm: 252 gcd: 12 3024
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
4?
Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?
hmmm, I honestly have no clue at all
Question 2.) If you were asked to state what you think to be the four most important numbers to all of mathematics. I'm not asking for your lucky number, or 42, or 1337, or any other quirky/"clever" response. I want to know, mathematically speaking, what you think the four most important numbers are. P.S., the answer is not 1,2,3, and 4. (Also, there are no right or wrong answers, and if you REALLY think it's 1,2,3,4, just justify your answer VERY well.)
Justify briefly.
well, I'd have to say 0, 10, 100, and 1000 are probably the most important numbers in my opinion
just think about it, multiply anything times 0 and you get 0, or add anything to 0 and the sum doesn't change from the original number
as for 10, 100, and 1000, they create the easiest numbers to multiply and divide by, simple as that, as well as in addition and subtraction
Set 2, concrete:
Question 1.) What is the lcm and gcd of the numbers 36 and 84? What is the product of 36 and 84?
lcm: 252 gcd: 12 3024
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
4?
Sunday the 10th
Well, since i read that post and i am pretty tired at the moment, I'm gonna not do this. So, I'm gonna use my homework pass.*uses homework pass*
10/10/10 omg triples
abstract:
1. I think the relationship of the GCD and LCM of a and b is that they are both multiples of a and b
2.In my opinion the 4 most important numbers in math could be 2,3,5,7 because we use prime factorization a whole lot in number theory, which applies to several types of math and these are the 4 smallest primes used for prime factorization
concrete:
1.what is the lcm and gcd of 36 and 84? what is the product?
36
2^2x3^2
84
2^2x3x7
lcm=2^2x3^2x7=252
gcd=12
36x84=3024
lcmXgcd=3024
2.(a)(b)=1024
lcm=4096
well given the information about 36 and 84 i come up with 1/4 sooooooooo... hah
1. I think the relationship of the GCD and LCM of a and b is that they are both multiples of a and b
2.In my opinion the 4 most important numbers in math could be 2,3,5,7 because we use prime factorization a whole lot in number theory, which applies to several types of math and these are the 4 smallest primes used for prime factorization
concrete:
1.what is the lcm and gcd of 36 and 84? what is the product?
36
2^2x3^2
84
2^2x3x7
lcm=2^2x3^2x7=252
gcd=12
36x84=3024
lcmXgcd=3024
2.(a)(b)=1024
lcm=4096
well given the information about 36 and 84 i come up with 1/4 sooooooooo... hah
Kaitlyn's Post 10/10/10
Set 1 abstract:
Question 1) They both find common numbers that are related to both a and b. The lcm can be divided by both a and b. The gcd can go into both a and b.
Question 2) I think the four most important numbers are 0, 1, 2, and 5. 0 because anytime you divide by 0 or multiply by 0, it will end up being no solution or 0. 1 is important because 1 can go into any number at all. When you divide a number by 1 it ends up being that number. Same when you divide by 1. 2 is important because half the numbers in the world can be divided by 2, since 2 goes into all even numbers. 5 is important because when you are dealing with prime factorization, this number shows up a lot.
Set 2 concrete:
Question 1) GCD=12 LCM= 252
The product of these two numbers is = 3024
Question 2) I think to find this you divide the product by the lcm because when i did it with question 1 it worked. So if this is how you do this, the answer would be 1/4. I dont see how thats possible but yeahhhh. But if you just divide the larger number by the smaller number, this answer would come out to be 4.
Question 1) They both find common numbers that are related to both a and b. The lcm can be divided by both a and b. The gcd can go into both a and b.
Question 2) I think the four most important numbers are 0, 1, 2, and 5. 0 because anytime you divide by 0 or multiply by 0, it will end up being no solution or 0. 1 is important because 1 can go into any number at all. When you divide a number by 1 it ends up being that number. Same when you divide by 1. 2 is important because half the numbers in the world can be divided by 2, since 2 goes into all even numbers. 5 is important because when you are dealing with prime factorization, this number shows up a lot.
Set 2 concrete:
Question 1) GCD=12 LCM= 252
The product of these two numbers is = 3024
Question 2) I think to find this you divide the product by the lcm because when i did it with question 1 it worked. So if this is how you do this, the answer would be 1/4. I dont see how thats possible but yeahhhh. But if you just divide the larger number by the smaller number, this answer would come out to be 4.
10/10/10
SET1-ABSTRACT
1) The relationship between gcd and lcm is that both a and b are either multiples or divisor of each other.
2)I think the four most important number are 2,3,5 and 7 because they are the four smallest prime numbers and they for used in prime factorization often.
SET2- CONCRETE
1)GCD(36,84)=12
LCM(36,84)=252
PRODUCT(252*12)=3024
2)I took the product and divided it by the lcm and got 1/4? so lol it might not be right
1) The relationship between gcd and lcm is that both a and b are either multiples or divisor of each other.
2)I think the four most important number are 2,3,5 and 7 because they are the four smallest prime numbers and they for used in prime factorization often.
SET2- CONCRETE
1)GCD(36,84)=12
LCM(36,84)=252
PRODUCT(252*12)=3024
2)I took the product and divided it by the lcm and got 1/4? so lol it might not be right
10/10/10
Set 1, abstract:
The relationship between them is that they are both multiples or factors or divisors of each other, a and b.
Question 2.) If you were asked to state what you think to be the four most important numbers to all of mathematics. I'm not asking for your lucky number, or 42, or 1337, or any other quirky/"clever" response. I want to know, mathematically speaking, what you think the four most important numbers are. P.S., the answer is not 1,2,3, and 4. (Also, there are no right or wrong answers, and if you REALLY think it's 1,2,3,4, just justify your answer VERY well.)
I think the four most important numbers are 0, 1, 2, and 10. 0 because when you multiply or do anything with 0, you get zero, or nothing happens to the number you are working with. 1 because when you multiply by this you get an identity sort of answer, exactly. 2 because I seem always to be working with the number 2. You use 2 for evens and primes and stuff, and 2 is just cool lol. 10 because big numbers are "derived" from 10, like 100, 1000, 10000, etc. The power of 10 rule is also important I think, that's why I said 10 is an important number.
Set 2, concrete:
Question 1.) What is the lcm and gcd of the numbers 36 and 84? What is the product of 36 and 84?
(36, 84)
36: 2x2x3x3
2^2 x 3^2
84: 2x2x3x7
2^2 x 3 x 7
lcm: 2^2 x 3^2 x 7 = 252
gcd: 2^2 x 3 = 12
36*84 = 3024
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
Yaaa I honestly don't know how to do this with the information given...when this was on the test, I just left it blank lol sorry.
10/10/10 hahhah
Question 1) They will contain the same number which means they are multiples or divisors of a and b
Question 2) I think the four most important numbers are 0 2 3 5 what have we been doing in number theory this whole time? dealing with prime factorization, so these are the smallest prime numbers. 0 is important because anything divided or multiplied by 0 is either impossible or 0. 2 is important because its also even so you can tell if a number is even and use it in prime factorization. 3, because so many numbers are multiples of 3. the same thing with 5, you can automatically tell if a number is divisible by 5 by looking at the end number, wether it be 5 ir zero.
set 2
question 1)
the GCD is 12, the lcm is 252
multiply them together and you get
product=3024
question 2)
B-Rob showed us how to find this, but it came out as 1/4, never got an answer like that so let's go with that.
Question 2) I think the four most important numbers are 0 2 3 5 what have we been doing in number theory this whole time? dealing with prime factorization, so these are the smallest prime numbers. 0 is important because anything divided or multiplied by 0 is either impossible or 0. 2 is important because its also even so you can tell if a number is even and use it in prime factorization. 3, because so many numbers are multiples of 3. the same thing with 5, you can automatically tell if a number is divisible by 5 by looking at the end number, wether it be 5 ir zero.
set 2
question 1)
the GCD is 12, the lcm is 252
multiply them together and you get
product=3024
question 2)
B-Rob showed us how to find this, but it came out as 1/4, never got an answer like that so let's go with that.
10/10/10 Post
Set 1.
1) The relationship between the gcd and lcm of a & b is that the gcd will always be a divisor of the lcm.
2) I think the most important numbers in mathematics are 2, 3, 5, and 7. I think this because they are the four prime numbers, and you can do many things with them. With 2 you can tell if something is even or odd by dividing that number by 2 and seeing if there is a remainder. If there is one, then the number is odd. I also think 3, 5, and 7 are important because they are the next smallest primes and are used very often when dealing with prime factorization.
Set 2.
1) LCM[36,84] = 12
GCD[36,84] = 252
36 * 84 = 3024 = 12 * 252 = LCM*GCD
2) a*b = 1024
lcm[a,b] = 4096
gcd[a,b] = ?
lcm*gcd = product
gcd = product/lcm
gcd = 1024/4096
gcd = 1/4
I don't think that there can be a non-integer gcd, so I therefore think this is probably wrong.
Ryan Breaud
1) The relationship between the gcd and lcm of a & b is that the gcd will always be a divisor of the lcm.
2) I think the most important numbers in mathematics are 2, 3, 5, and 7. I think this because they are the four prime numbers, and you can do many things with them. With 2 you can tell if something is even or odd by dividing that number by 2 and seeing if there is a remainder. If there is one, then the number is odd. I also think 3, 5, and 7 are important because they are the next smallest primes and are used very often when dealing with prime factorization.
Set 2.
1) LCM[36,84] = 12
GCD[36,84] = 252
36 * 84 = 3024 = 12 * 252 = LCM*GCD
2) a*b = 1024
lcm[a,b] = 4096
gcd[a,b] = ?
lcm*gcd = product
gcd = product/lcm
gcd = 1024/4096
gcd = 1/4
I don't think that there can be a non-integer gcd, so I therefore think this is probably wrong.
Ryan Breaud
10/10/10
Set 1:
1.) The gcd and lcm usually have common multiples or one of the numbers is the divisor of the other. For example: gcd and lcm (24, 54)
*find the prime factorization first and you get that
24's prime factorization is 2^3(3)
54's prime factorization is 3^3(2)
LCM = 216
GCD = 6
*In this case, 6 is a divisor of 216
2.) I think the four most important numbers in mathematics are 0, 1, 2, and 3.
0 is important because often when it is involved in some problems, the answer may be 0 or possibly undefined. i.e. whenever 0 is involved, several things cancel out because of it. 1 is also important because it is a simple number with simple rules to it..as in if it were involved in addition or subtraction, it doesn't dramatically change the solution to a problem; whereas when it's involved in multiplication or division, it doesn't change the answer at all because when multiplying or dividing a # by 1, you get that #. 2 is also important because it is the the number that can go evenly into most numbers (well I think so); especially since 2 is in the majority of categories of numbers, i.e.--2 is an integer, a whole #, natural #, even, power of 2, prime..etc. Lastly, 3 is another important number because it aquires some of the same characteristics as 2...3 is an integer, whole #, natural #, prime, odd. Also 3 is used when cubing a number or cuberooting it, as 2 is used when you want to find half of something or when you want to square a # or square root it.
Set 2:
1.) (36, 84)
*To find the gcd and lcm, you first find the prime factorization of both numbers.
36's prime fact. is 2^2(3^2)
84's prime fact. is 2^2(3)(7)
*Using the prime factorizations you find that the GCD = 12 and LCM = 252
*The product of 36 and 84 (which is also the product of the GCD & LCM) is 3024
2.) Okay for this question, I have no idea what to do because I tested it out with the gcd and lcm you gave in question 1 and it worked (because you take the product and divide it by the lcm)..but for this one I got 1/4...So I'm thinking maybe you multiply 1/4 by 1024 and get that the gcd is 256? (that's most likely wrong, but I tried..)
1.) The gcd and lcm usually have common multiples or one of the numbers is the divisor of the other. For example: gcd and lcm (24, 54)
*find the prime factorization first and you get that
24's prime factorization is 2^3(3)
54's prime factorization is 3^3(2)
LCM = 216
GCD = 6
*In this case, 6 is a divisor of 216
2.) I think the four most important numbers in mathematics are 0, 1, 2, and 3.
0 is important because often when it is involved in some problems, the answer may be 0 or possibly undefined. i.e. whenever 0 is involved, several things cancel out because of it. 1 is also important because it is a simple number with simple rules to it..as in if it were involved in addition or subtraction, it doesn't dramatically change the solution to a problem; whereas when it's involved in multiplication or division, it doesn't change the answer at all because when multiplying or dividing a # by 1, you get that #. 2 is also important because it is the the number that can go evenly into most numbers (well I think so); especially since 2 is in the majority of categories of numbers, i.e.--2 is an integer, a whole #, natural #, even, power of 2, prime..etc. Lastly, 3 is another important number because it aquires some of the same characteristics as 2...3 is an integer, whole #, natural #, prime, odd. Also 3 is used when cubing a number or cuberooting it, as 2 is used when you want to find half of something or when you want to square a # or square root it.
Set 2:
1.) (36, 84)
*To find the gcd and lcm, you first find the prime factorization of both numbers.
36's prime fact. is 2^2(3^2)
84's prime fact. is 2^2(3)(7)
*Using the prime factorizations you find that the GCD = 12 and LCM = 252
*The product of 36 and 84 (which is also the product of the GCD & LCM) is 3024
2.) Okay for this question, I have no idea what to do because I tested it out with the gcd and lcm you gave in question 1 and it worked (because you take the product and divide it by the lcm)..but for this one I got 1/4...So I'm thinking maybe you multiply 1/4 by 1024 and get that the gcd is 256? (that's most likely wrong, but I tried..)
october 10 post
set 1:
1) the relationship between the lcm and gcd of two positive integers a & b, is that both numbers are either multiples or divisors of a & b.
2)I think one of the 4 most important numbers is 0. because when you do anything with 0, you usually end up with 0. Another important number is 1, because when multiplying or dividing by one, you end up with the OTHER number. Another important number is 2 because it is the first prime number, the first even number, you can get ANY even number if you multiply anything by 2. it is used for formulas to find every odd/even number. it probably is the MOST important. And I think another important number is 5. just because it seems like that would be the other number
set 2:
1) lcm=252... gcd=12... product=3024
2)i honestly don't know how to find the gcd with only the information given to me..
1) the relationship between the lcm and gcd of two positive integers a & b, is that both numbers are either multiples or divisors of a & b.
2)I think one of the 4 most important numbers is 0. because when you do anything with 0, you usually end up with 0. Another important number is 1, because when multiplying or dividing by one, you end up with the OTHER number. Another important number is 2 because it is the first prime number, the first even number, you can get ANY even number if you multiply anything by 2. it is used for formulas to find every odd/even number. it probably is the MOST important. And I think another important number is 5. just because it seems like that would be the other number
set 2:
1) lcm=252... gcd=12... product=3024
2)i honestly don't know how to find the gcd with only the information given to me..
Friday, October 8, 2010
Blog Prompt, October 8, 2010
Hey everyone, sorry about last week. I managed to completely forget to post a prompt.
Anyways, here's this week's. It should be relatively laid back and mostly opinionated:
All questions are required:
Set 1, abstract:
Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?
Question 2.) If you were asked to state what you think to be the four most important numbers to all of mathematics. I'm not asking for your lucky number, or 42, or 1337, or any other quirky/"clever" response. I want to know, mathematically speaking, what you think the four most important numbers are. P.S., the answer is not 1,2,3, and 4. (Also, there are no right or wrong answers, and if you REALLY think it's 1,2,3,4, just justify your answer VERY well.)
Justify briefly.
Set 2, concrete:
Question 1.) What is the lcm and gcd of the numbers 36 and 84? What is the product of 36 and 84?
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
Anyways, here's this week's. It should be relatively laid back and mostly opinionated:
All questions are required:
Set 1, abstract:
Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?
Question 2.) If you were asked to state what you think to be the four most important numbers to all of mathematics. I'm not asking for your lucky number, or 42, or 1337, or any other quirky/"clever" response. I want to know, mathematically speaking, what you think the four most important numbers are. P.S., the answer is not 1,2,3, and 4. (Also, there are no right or wrong answers, and if you REALLY think it's 1,2,3,4, just justify your answer VERY well.)
Justify briefly.
Set 2, concrete:
Question 1.) What is the lcm and gcd of the numbers 36 and 84? What is the product of 36 and 84?
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
Sunday, October 3, 2010
Blog Prompt #4
Question 1:
1332
6x222
2x3 2x111
3x37
Answer: 2x3^2x37
Question 2:
240, 120x2, 60x2, 30x2, 15x2, 5x3 Prime Factorization= 2^4x3x5
840, 420x2, 210x2, 105x2, 21x5, 7x3 Prime Factorization= 2^3x3x5x7
GCD: 4
LCM: 1680
Question 3:
133 and 103 are both prime numbers. I added the factors together to see if anything can go into them, and then checked by regular division.
Question 4:
2= 1
3= 1
5= 0
13= 9
I did not feel like using the prime factorization for this method so i am not going to lie, I just did regular divison with some help from my calculator.
1332
6x222
2x3 2x111
3x37
Answer: 2x3^2x37
Question 2:
240, 120x2, 60x2, 30x2, 15x2, 5x3 Prime Factorization= 2^4x3x5
840, 420x2, 210x2, 105x2, 21x5, 7x3 Prime Factorization= 2^3x3x5x7
GCD: 4
LCM: 1680
Question 3:
133 and 103 are both prime numbers. I added the factors together to see if anything can go into them, and then checked by regular division.
Question 4:
2= 1
3= 1
5= 0
13= 9
I did not feel like using the prime factorization for this method so i am not going to lie, I just did regular divison with some help from my calculator.
Alaina's post, 3 Oct. 2010
Question 1:
What is the prime factorization of 1332?
1332->3, 444->2, 222->2, 111->3, 37
2*32*37
Question 2:
What is the gcd and lcm of 240 and 840?
GCD: 240->2, 120->2, 60->2, 30->2, 15->3, 5
prime factorization=24*3*5
840->2, 420-> 2, 210->2, 105->5, 21->3, 7
prime factorization=23*3*5*7
4*1*1=4
LCM:24*3*5*7
16*3*5*7=1680
Question 3:
Is 133 prime? What about 103? How did you find out that it is/is not (without looking it up)?
Both 133 and 103 are prime. You cannot find the prime factorization of either. None of the small primes go into either 133 or 103.
Question 4:
What is the remainder whe 4803925 is divided by 2? When it is divided by 3? By 5? By 13? How did you figure each out?
4803925/2= remainder of 1
4803925/3= remainder of 1
4803925/5= remainder of 0
4803925/13= remainder of 9
I really didn't feel like using the prime factorization method so I just divided. Finding the remainder when dividing by 2 and 5 were very easy. 5 goes into anything that ends in a 5 or 0 evenly. 2 goes into anything that is even so because it is odd, the remainder is 1. 3 goes into all of the numbers except 4803925 so i only divided 3 into 25-> remainder of 1. 13 was the hardest of them. it just required some simple long division.
What is the prime factorization of 1332?
1332->3, 444->2, 222->2, 111->3, 37
2*32*37
Question 2:
What is the gcd and lcm of 240 and 840?
GCD: 240->2, 120->2, 60->2, 30->2, 15->3, 5
prime factorization=24*3*5
840->2, 420-> 2, 210->2, 105->5, 21->3, 7
prime factorization=23*3*5*7
4*1*1=4
LCM:24*3*5*7
16*3*5*7=1680
Question 3:
Is 133 prime? What about 103? How did you find out that it is/is not (without looking it up)?
Both 133 and 103 are prime. You cannot find the prime factorization of either. None of the small primes go into either 133 or 103.
Question 4:
What is the remainder whe 4803925 is divided by 2? When it is divided by 3? By 5? By 13? How did you figure each out?
4803925/2= remainder of 1
4803925/3= remainder of 1
4803925/5= remainder of 0
4803925/13= remainder of 9
I really didn't feel like using the prime factorization method so I just divided. Finding the remainder when dividing by 2 and 5 were very easy. 5 goes into anything that ends in a 5 or 0 evenly. 2 goes into anything that is even so because it is odd, the remainder is 1. 3 goes into all of the numbers except 4803925 so i only divided 3 into 25-> remainder of 1. 13 was the hardest of them. it just required some simple long division.
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