Factors are numbers that divide evenly into another number, and a prime factor is a factor that is a prime number. A factor tree is a tool that breaks down any number into its prime factors. Factor trees are helpful tools for students because they provide a graphic representation of the prime factors that can divide into a given number. Factor trees are so named because once created, they look somewhat like a tree.

The worksheets below give students practice in creating factor trees. For example, the free printables list numbers such as 28, 44, 99, or 76 and ask students to create a factor tree for each. Some of the worksheets provide some of the prime factors and ask students to fill in the rest; others require students to create factor trees from scratch. In each section, the worksheet is printed first with an identical worksheet below it listing the answers to make grading easier.

## Prime Factor Tree Worksheet No. 1

Find out how much students know about creating factor trees by having them complete this worksheet first. It requires students to create each factor tree from scratch.

Before having students start this worksheet, explain that when factoring the numbers, there is often more than one way to do so. It won’t matter which numbers they use because they will always end up with the same prime factors of the number. For example, the prime factors for 60 are 2, 3 and 5, as the example problem demonstrates.

## Prime Factor Tree Worksheet No. 2

For this worksheet, students find the prime numbers for each number listed using a factor tree. If students are struggling, this worksheet may help them master the concept. It provides some of the factors, and students fill in the rest in provided blank spaces.

For example, in the first problem, students are asked to find the factors of the number 99. The first factor, 3, is listed for them. The students then find the other factors, such as 33 (3 x 33), which factors further into the prime numbers 3 x 3 x 11.

## Prime Factor Tree Worksheet No. 3

This worksheet gives struggling students more help in mastering factor trees because some of the prime factors are provided for them. For example, the number 64 factors into 2 x 34, but students can further factor that number into prime factors of 2 x 2 x 17, because the number 34 can factor into 2 x 17.

## Prime Factor Tree Worksheet No. 4

This worksheet provides some of the factors to help students create factor trees. If students are struggling, explain that the first number, 86, can only factor into 43 and 2 because both of those numerals are prime numbers. By contrast, 99 can factor into 8 x 12, which can further factor into (2 x 4) x (2 x 6), which further factors into the prime factors (2 x 2 x 2) x (2 x 3 x 2).

## Prime Factor Tree Worksheet No. 5

Finish your factor tree lesson with this worksheet that also gives students some of the factors for each number. For further practice, have students complete these worksheets that let them find the prime factors of numbers without using factor trees.