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.

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.

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.

 

How to Print or Save these sheets

how to print information image printer

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

How to Print or Save these sheets

how to print information image printer

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

Math-Salamanders.com

Math Salamanders Main Logo

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.


New! Comments

Have your say about the Math resources on this page! Leave me a comment in the box below.
 

Math Salamanders Copyright Information.

Math Salamanders Shop

math salamanders shop logo

Looking for some fun printable math games?

We have some great games for you to play in our Math Games e-books!

NEW Online Age Calculator

Online Age Calculator image

Do you know how old you are...in weeks? days? hours?

Are you more than a million minutes old?

Find out how old you are to the nearest second!

NEW Fraction Calculators

We have updated and improved our fraction calculators to show you how to solve your fraction problems step-by-step!

Take a look and try them out!

Adding Fractions Calculator image Subtracting Fractions Calculator image Multiply Fractions Calculator image Divide Fractions Calculator image

Some of our TOP pages!

Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child


Support Us

If you are a regular user of our site and appreciate what we do, please consider making a small donation to help us with our costs.

Get a free sample copy of our Math Salamanders Dice Games book with each donation!

FUN Math Games

Math Games Learning Games Captain Salamander

Looking for a fun and motivating way to learn and practice math skills?

Why not try one of our free printable math games with your students!