Factor Tree Worksheets

Welcome to our Factor Tree Worksheets page.

Here you will find our selection of worksheets involving using factor trees for factorize numbers.

We have a range of sheets at different levels of difficulty.

Factor Tree Worksheets

On this page we have worksheets using factor trees to factorize a range of numbers.

We also have a link to our Prime Factorization Calculator which will quickly and easily show you all the prime factors of any number.

Using these factor tree worksheets will help your child to:

  • use and understand factor trees;
  • factorize a range of different numbers up to 100 and beyond.

These sheets are aimed at students from 6th grade and upwards.

What is a factor tree?

A factor tree is a visual way of factorizing a number and showing you all the prime factors that multiply together to make the number.

Factor trees have several rules:

  • you cannot use the number 1 in a factor tree (or the tree just goes on forever)
  • the two numbers underneath each rectangle must multiply together to make the number in the rectangle above.

What does a factor tree look like?

Let's have a look at a couple of examples.

Example 1) Complete the factor tree below and write down the prime factorization of 12.

factor tree example 1a image

  • The number in the top rectangle is the number we are trying to find the factors for.
  • The numbers in the circles are the prime factors that multiply together to give the number above.
  • The numbers in the other rectangles are composite (non-prime) numbers that we still need to find the factors for.

We know that 12 = 2 x 6 and 12 = 3 x 4 (we cannot use 1 in a factor tree!)

We can use either of these equations - it does not matter which one.

Let's use 12 = 2 x 6. So the prime factor is 2 and the composite factor is 6.

This gives us:

factor tree example 1b image

Now we only have the 6 left to factorize.

We know that 6 = 1 x 6 and 6 = 2 x 3.

We cannot use 1 in a factor tree, so that leaves us with 6 = 2 x 3.

This gives us:

factor tree example 1c image

The prime factors of 12 are 2, 2, and 3.

This means that 12 = 2 x 2 x 3 (or 22 x 3) as a product of prime factors (prime factorization.

Example 2) Let us go back to Example 1) and factorize it in a different way.

This time we will factorize 12 as 3 x 4 instead of 2 x 6.

This gives us:

factor tree example 1d image

Now we only have the 4 left to factorize.

We know that 4 = 1 x 4 and 4 = 2 x 2.

We cannot use 1 in a factor tree, so that leaves us with 4 = 2 x 2.

This gives us:

factor tree example 1e image

The prime factors of 12 are still 2, 2, and 3.

So we still end up with 12 = 2 x 2 x 3 (or 22 x 3) as a product of prime factors (prime factorization.

So we still have the same answer as Example 1) but the factor trees have some different numbers in.

The Factor Tree in Example 1) has a 6, and the Factor Tree in Example 2) has a 4.

This does not matter - the important thing is that the numbers in the circles (the prime factors) are the same in both examples.

Factor Tree Worksheets

All the worksheets have answers provided. However, as in the example above, the answers are not unique - you can have several different factor trees for numbers.

The important thing is that the prime factorization of each number has to match the answer provided.

The sheets are graded with the easiest sheets first.

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

What is prime factorization?

To find out more about prime factorization, including how it works and to look at some worked examples, take a look at our prime factorization support page.

Prime Factorization Worksheets

As well as factor tree worksheets, we also have a collection of prime factorization worksheets.

These worksheets are harder than the sheets on this page, and require an understanding of prime factorization.

We have prime factorization challenges and also prime factorization riddles here too.

Prime Factorization Calculator

Our prime factorization calculator will help you factor any number into a product of its prime factors.

It will show the answer in exponential form as well as standard form.

You can use this calculator to check that your prime factors in your factor trees are correct.

Greatest Common Factor Worksheets

As well as our calculator, we also have a range of greatest common factor worksheets.

These sheets have been designed for 6th and 7th grade students.

They will help students learn and practice finding the greatest common factor of numbers up to 100.

Least Common Multiple Worksheets

We have a range of worksheets on how to find the least common multiple of two or three numbers.

The sheets vary in difficulty, and are suitable for 6th grade and up.

5th and 6th Grade Fractions Worksheets

Here you will find a range of more complex Fraction Worksheets for 5th and 6th graders.

At 5th Grade level, children are introduced to adding and subtracting fractions with different denominators. They know and can use equivalent fractions, and can multiply a fraction by whole numbers, as well as adding mixed numbers.

Using these sheets will help your child to:

  • add and subtract fractions and mixed numbers;
  • understand how to multiply fractions by a whole number;
  • understand how to multiply two fractions together, including mixed fractions;
  • understand the relationship between fractions and division;
  • know how to divide fractions and mixed fractions;
  • convert decimals to fractions.
 

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How to Print or Save these sheets

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Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!

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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.


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