Question

Why is it helpful to write a number as a product of primes

Answer 1

because if you are multiplying or dividing, you can regroup numbers to make it easy so exg
80 times 45 might look scary but it is really 2 times 2 times 2 times 2 times 3 times 3 times 5 times 5
regroup to make
(2 times 5) times (2 times 5) times (2 times 2 times 3 times 3)=10 times 10 times (6 times 6)=10 times 10 times 36=3600

dividing
188/132
188=2 times 2 times 47
44=2 times 2 times 3 times 11
so it becomes (2 times 2)/(2 times 2) times (47/(3 times 11))=1 times 47/33=47/33