Prime Factorization

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Understanding Factors and Multiples Worksheets

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.

Alternative factor tree for 24

 and  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