Prime Factorization Question

jman115

New member
When I teach GCF to students, I show them how to find via the prime factorization and explain to them how the PF can get you all the factors of a number by multiplying different combinations of the Prime Factors and then proceed to explain why they are supposed to multiply the common Prime factors for the gcf.

My question is, why does multiplying different combinations of the prime factors get you ALL of the number's factors?

masters

Active member
When I teach GCF to students, I show them how to find via the prime factorization and explain to them how the PF can get you all the factors of a number by multiplying different combinations of the Prime Factors and then proceed to explain why they are supposed to multiply the common Prime factors for the gcf.

My question is, why does multiplying different combinations of the prime factors get you ALL of the number's factors?
Hi jman115,

I know you know this already, but every composite number can be factored into the products of only prime numbers. Any combination of products with these prime factors will yield a composite factor of the original number.

jman115

New member
"Any combination of products with these prime factors will yield a composite factor of the original number." I stated this fact in my opening thread.

I am asking why this works. When you multiply all combinations of the prime factors you get all the composite factors of that number. I want to know why this works.