How do you know when you have prime factorization?

Answer 1

Knowing When Factorization is Prime

Factorization is prime factorization when all the factors are prime numbers. If there is just one composite number in the factorization, it is not prime.

A couple of examples:

12 - 2 X 6 = 12. 2 is prime, but 6 is composite, so more factoring is needed.

2 X 2 X 3 = 12. Numbers 2 and 3 are prime, so prime factorization is complete.

Always starting with the lowest factor of the number (except for 1) makes this easy.

For example, the number 100. You can start with any of its factors, but the lowest one is 2, so start with it.

100 - 2 X 50 = 100. 50 is a composite number, so it must be factored. 2 is the lowest factor (besides 1), so use it.

2 X 2 X 25 = 100. Now, 25 needs to be factored, but the lowest factor is not 2, but 5, so use it.

2 X 2 X 5 X 5 All numbers are now prime, so the prime factorization of 100 is:

2 X 2 X 5 X 5. You can also write it with exponents like this: 22 X 52