Prime Factorization

Prime factorization means finding all the prime numbers that are factors of a number. A composite number can be  written as a product of all of its prime factors.

Example of Prime Factorization

The number 24 can be written as a product of prime numbers

24 = 2 x 2 x 2 x 3

It is called the prime factorization of 24.

Factor Trees

A factor tree shows the prime factors of a composite number in a "tree-like" form. Drawing factor trees is a good way of doing prime factorization.

You can make different factor trees to find the same prime factorization. Look at the two examples below.

Factor tree for 24 and Alternative factor tree for 24 both give the same prime factorization.

Other Examples of Factor Trees

Factor tree for 30 shows 2 x 3 x 5 as the prime factorization of 30. Note: You could get the same result with a different tree!

Factor tree for 32 shows 2 x 2 x 2 x 2 x 2 as the prime factorization of 32.

Prime Factorization Worksheets