What is a prime factorization?

Prime factorization is finding the prime factors you need to multiply together to get the original number. A prime factor is a factor that is a Prime number.

Example:

The prime factorization of 30 is 2 x 3 x 5
Prime factorization is breaking a number into smaller prime divisors which multiply to equal the original number.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.