C. Prime Factorization

The prime factorization of a number involves breaking a number into its prime factors. One way to show prime factorization visually is to use a factor tree. Factor trees can also help with organization.

Prime Factorization
expressing a number as the product of its prime factors

 

Example 1

What is the prime factorization of 140?

Start by dividing 140 by the smallest prime number.

140 ÷ 2 = 70

Because 70 is not a prime number, it must be further factored. Divide 70 by the smallest prime number.

70 ÷ 2 = 35

But, 35 is not a prime number, so 35 must be further factored. The smallest prime factor of 35 is 5.

35 ÷ 5 = 7

The number 7 is a prime number, so 140 has been fully factored and can be written as follows:

140 = 2 × 2 × 5 × 7

Organize and represent your work using a factor tree. Note that every factor in red is a prime number.

The prime factorization of 140 = 2 × 2 × 5 × 7.

Divide the original number by the smallest prime number and write the answer below the original number. Continue the pattern by dividing the next factor by the smallest prime number until all the values are prime themselves.


A factor tree is one method of organizing and representing the prime factorization of a number. The following is another method of prime factorization.

The prime factorization of 140 = 2 × 2 × 5 × 7.