Sorry this one is late, I've had a busy weekend and have been preoccupied.
Okay, this week should be short and relatively simple. There are a total of 9 calculations for you to undergo, none of which are difficult nor lengthy. Brief explanation/work will suffice, but I do want to see something.
(Please show your work (briefly))
Question 1:
What is the prime factorization of 1332?
Question 2:
What is the gcd and lcm of 240 and 840?
Question 3:
Is 133 prime? What about 103? How did you find out that it is/is not (without looking it up.)
Question 4:
What is the remainder when 4803925 is divided by 2? What is it when it is divided by 3? By 5? By 13?
How did you figure each of these out?
Question 1: What is the prime factorization of 1332?
ReplyDelete1332
3 444
111 4
3 37 2 2
(2^2)(3^2)(37)
Question 2: What is the gcd and lcm of 240 and 840?
First thing I'd do is find the prime factorization, but i could be wrong(which I doubt because I'm a genious).
240: (2^4)(3)(5)
840: (2^3)(3)(5)(7)
For the gcd you take every common number's smallest value. So:
(2^3)(3)(5)=120
So, 120 is the gcd. Lcm you take every value at its highest exponent.
(2^4)(3)(5)(7)=1680
1680 is the LCM.
Question 3: Is 133 prime? What about 103?
Not looking it up...
My strategy would be just to check. I'd try numbers up to around the square root of that number so for 133:
2(no), 3(no), 4(no), 5(no), 6(no), 7(yesh)
So, 7 and 19 are factors meaning 133 is not prime.
103 now:
2(no), 3(no), 4(no), 5(no),... 9(no), 10(no)
At this point i'd assume that this number is prime. The square root of 103 is between 10 and 11 and thats where i'd stop checking at.
Question 4: What is the remainder of 4803925 when divided by 2? 3? 5? 13?
My strategy is to find out if its a factor first off. If not, just divide.
2: 2401962R1
3: 1601308R1
5: NO Remainder because 5 is a factor.
13: 377994R3
So, those are my strategies. The first two are shortcuts that I learned in class and the last 2 are my hard headed ways of doing things the long way even though I know there are shortcuts.