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

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