A prime factorization of a number is a unique (only one possible) listing of all the prime numbers whose product gives you that number. Every number has a prime factorization, and it's not shared with any other number. The prime factorization of 12 is 2 * 2 * 3 = 2^2 * 3. Those three factors are the only three prime factors that result in a 12. A prime factorization helps you find common factors between two or more expressions. The prime factorization of a prime number is just that number, because 1 isn't prime.

To find the prime factorization of a number, you can start by thinking of any two numbers whose product is that number, and then take each of those two numbers and think of two numbers whose product is each of them, and so on until only prime numbers are being multiplied.