# Prime Factorization Numbers

A **prime factor** is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. Now we can also use what’s called prime factorization for numbers which actually consist of using factor trees. Prime factorization is a process of writing all numbers as a product of primes. So, for example, say if we have something like the number 20. We can break that down into two factors. We can say, “well, that’s 4 times 5.” And notice, 5 is a prime number. 4 is not a prime number. That’s called a composite number. But if we break these things down, then we‘ve got 2 times 2 equals 4, and these 2’s are actually prime numbers, so we can circle those. So, we can say the prime factorization of 20 actually equals 2 times 2 times 5. And you don’t always have to do the 4 times 5. You could break 20 down into 2 times 10. Whichever way you’d like is fine. So, notice 2 times 10, that 2 is prime, whereas the 10 is composite. So we can break that down into 2 times 5. So we’re circling all the prime numbers that we see. And, again, we’ve got 2 times 2 times 5 equaling 20. So that’s prime factorization.