Mal's Whatever post...

Question 1:
What is the prime factorization of 1332?
1332
2*666
2*2*333
2*2*3*111
2*2*3*3*37

2^2*3^2*37

Question 2:
What is the gcd and lcm of 240 and 840?
Prime factorization of each is:

240=2^4**3*5
840=2^3*3*7*5

so the gcd after taking all of the common numbers between the factorization and the lowest of those and multiplying it together(if that makes any sense) gives you:

gcd(240, 840)=120

now for lcm, you take the highest exponent between the two over every numbers...so this gives you:

lcm(240, 840)=1680

Question 3:
Is 133 prime? What about 103? How did you find out that it is/is not (without looking it up.)

Okay. so what I did for this thing is use the Sieve of Eran...something. So after writing the first couple of rows of the sieve starting from 101, I went through that process where you start with 2 and so on, crossing out all the multiples of prime numbers. Okay> so...the following I believe to be true:

133-composite...it gets canceled out by 7 in the sieve
103-prime. nothing goes into it.

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?

So when I saw this, I was extremely tempted to just plug it in my calculator. That said, I did not.

I then began just dividing using long division (imagine that!). However, I do recognize that I can just find the prime factorization of it and put that over the number I'm dividing by. Again though, I relized that for say 5, I could just use my divisibility rules...5 obviously will go into a number evenly if it ends in what? 0 or 5 right? and this number does...so the remainders are as follows:

2:1
3:1
5:0
13:9