What's a better definition for prime factorization to me understand it? ?

It's really simple, a prime number is simply a number that can only be DIVIDED by 1 or itself. So 5 can't be divided by anything but 5 or 1. Now going from this when doing Prime FACTORIZATION, you have to find 2 numbers that multiply to the number you were given. Let's say your told to find the prime factor of 12. What divides into it? Well 6x3 does but 6 is not a prime number. But 2x2x3 = 12 and it uses only prime numbers. Hope this helps!