Prime Factorization Worksheets

Welcome to our Prime Factorization Worksheets page.

Here you will find our selection of worksheets involving finding prime factorizations for a range of numbers, and for solving prime factor problems.

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

Prime Factorization Worksheets

Using these factor tree worksheets will help your child to:

  • practice prime factorization of a range of numbers;
  • solve problems involving prime factorization;
  • use and understand exponential notation.

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

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

There is also a quick quiz at the bottom of the page where you can test your skill at prime factorization and get immediate feedback!

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.

Examples of Prime Factorization

Example 1) Find the prime factorization of 40.

40 is even, so we know that 2 is a factor (as well as being prime)

40 = 2 x 20.

Now we move on to the number 20.

Again 20 is even, so 2 is a factor.

20 = 2 x 10

So 40 = 2 x 20 = 2 x 2 x 10

Now we factorize 10 into 2 x 5 (both prime numbers) and we cannot go any further, as all the numbers are prime.

So 40 = 2 x 20 = 2 x 2 x 10 = 2 x 2 x 2 x 5

Our final answer is 40 = 2 x 2 x 2 x 5 = 23 x 5

Example 2) Find the prime factorization of 45.

45 is odd, so 2 is not a factor.

As the number ends in a 5 we know that 5 is a factor.

45 = 5 x 9.

Now we have to factorize 9.

9 = 3 x 3 (which is a prime number).

This gives us:

45 = 5 x 9 = 5 x 3 x 3

Our final answer is 45 = 3 x 3 x 5 = 32 x 5

Example 3) Find the prime factorization of 126.

126 is even, so 2 is a factor.

126 = 2 x 63

Now we need to factorize 63.

63 = 7 x 9.

7 is prime, but 9 is not

Now we have to factorize 9.

9 = 3 x 3 (which is a prime number).

This gives us:

126 = 2 x 63 = 2 x 7 x 9 = 2 x 7 x 3 x 3

Our final answer is 126 = 2 x 3 x 3 x 7 = 2 x 32 x 7

Prime Factorization Worksheets

All the worksheets have answers provided. The answers are given with the factors in ascending order.

The sheets get gradually harder in each section.

We have split the sheets into 3 different sections:

  • Our first section involves straightforward prime factorization of different numbers.
  • Our next group of sheets involves solving prime factorization riddles.
  • Our final group of sheets involves finding all possibilities in our prime factorization challenges.

Prime Factorization Worksheets - 1st Section

  • The two sheets just has straightforward prime factorization of a range of numbers.
  • The third sheet is harder, and involves using exponential notation and looking at prime factorization from different starting points

Prime Factorization Worksheets - Riddles - 2nd Section

These sheets involve solving prime factorization riddles.

There are 2 riddles on each sheet and 8 possible answers.

By correctly working out the clues in each riddle, all the incorrect answers are eliminated leaving just one correct answer.

Prime Factorization Worksheets - Challenges - 3rd Section

Our prime factorization challenges are a great way to stretch more able students.

The challenges involve finding all possible numbers that have certain features involving prime factors.

Prime Factorization Walkthrough Video

This short video walkthrough shows several problems from our Prime Factorization Worksheet 3 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on this page, check out the video!

More Recommended Math Worksheets

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

Factors and Multiples Worksheets

We have worksheets to help you understand more about factors and multiples.

They are aimed at a 4th/5th grade level.

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.

Factor Tree Worksheets

Using factor trees is a great visual way to understand prime factorization.

The worksheets on the link below are at an easier level to the sheets on this page and help children learn all about factor trees and prime factors.

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.

Sieve of Erastosthenes

The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.

Want to find out more about primes?

Take a look at our Prime Number page which clearly describes what a prime numbers is and what they are not.

There are also many different questions about prime numbers answered, as well as information about the density of primes.

Divisibility Rules 1-10 Chart

We have a range of charts which can help you determine whether a number between 1 and 10 is a factor of a number.

6th Grade Mental Math Quizzes

Here you will find a range of printable mental math 6th grade quizzes for your child to enjoy.

Each worksheet tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

Prime Factorization Online Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge of prime factorization with numbers up to 120.

 

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

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