Question

How is finding the factors of a number different from finding the prime factorization of a number?

Answer 1

Factors are any numbers (prime or composite) that go into a given number. Prime factorization is finding all the prime numbers that go into the number and how many times each prime number goes into it. For example, factors of 16 are: 1, 2, 4, 8, 16. The prime factorization of 16 is: 2*2*2*2.
Another example:
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Prime factorization of 42: 2*3*7