How to Do Prime Factorization

What Is Prime Factorization?

Prime factorization is finding prime numbers that, when multiplied, equal the original number.

Method

The best and easiest way to do prime factorization is to use a factor tree.

Step 1:

In this example, we will look for the prime factorization of 90. Using a factor tree, we will find all of the prime numbers that when multiplied, equal 90, and circle them. The prime factors of 90 are 2, 3, 3, and 5.

Step 2:

Now that you've found how the prime numbers, you now you have the prime factorization of 90. All you have to do is put it into correct form. The answer to the prime factorization of 90 is : 90 = 2 • 3 • 3 • 5

But, a better way to put it is : 90 = 2 • 3² • 5

Prime Factorization of Prime Numbers

If a number is already prime, the prime factorization of that number is itself. For example, the prime factorization of 13 = 13 because 1 and 13 are the only prime numbers that can be divided evenly by 13.