Heather's #4

1.) Prime Factorization of 1332:
1332
2(666)
2(333)
3(111)
3(37)
= 2^3 x 3^3 x 7

2.) GCD (240, 840)
*Prime factorizations:
240:
2(120)
2(60)
2(30)
2(15)
3(5)
=2^4 x 3 x 5

840:
2(420)
2(210)
2(105)
3(35)
5(7)
= 2^3 x 3 x 5 x 7
*To find the GCD, you look at the prime factorization of 240 and 840. You cross out the numbers they do not have in common (so for this one you would rule out 7). Then you multiply the numbers in common that have the least exponent.
*So you would take 2^3 x 3 x 5
GCD = 120

LCM (240, 840)
*For this you still use the prime factorization of both numbers but instead you multiply each number there with the highest exponent (and you include every number present, whether they have it in common or not)
*So you would get 2^4 x 3 x 5 x 7
LCM = 1680

3.) Is 133 prime? NO...Is 103 prime? YES!
*I simply used divisibility rules. And 133 is composite because I found that 7 can go into it evenly, whereas nothing can go into 103.

4.) Remainders when 4803925...
*is divided by 2 -- remainder is 1
*divided by 3 -- remainder is also 1
*divided by 5 -- there is NO remainder. 5 goes in evenly (divisibility rules say that 5 can go into any number that ends in a 5 or zero evenly)
*divided by 13 -- remainder is 9
**I found these out simply by dividing 4803925 by every number given, except 5.