Greatest Common Factor Worksheet

On this page we have worksheets for finding the greatest common factor of 2 or 3 numbers up to 100.

We also have a link to our Greatest Common Factor Calculator which will quickly and easily find the greatest common factor between 2 or more numbers, and also show you the working out along the way.

Using these greatest common factor worksheets will help your child to:

• understand what the greatest common factor is;
• find the greatest common factor between two numbers up to 100.

First of all let us think about what a factor is.

A factor is a number which divides into another number with no remainder.

In other words, you can multiply a factor by a whole number to get to the number it is a factor of.

• 12 = 3 x 4, so 3 and 4 are both factors of 12.
• 25 = 5 x 5 so 5 is a factor of 25
• 60 = 12 x 5, so 5 and 12 are both factors of 60.

You will also note that 1 is a factor of all integers.

Now a common factor is a number that several numbers have in common.

And the Greatest Common Factor between two numbers is the largest number that is a factor of both numbers.

And the Greatest Common Factor between lots of numbers, is the largest factor that all the numbers have in common.

The Greatest Common Factor is the same as the Highest Common Factor, and the Greatest Common Divisor.

It is often abbreviated to the GCF.

If there are no other common factors, then the gcf is 1 (as 1 is a factor of all positive integers.)

If the greatest common factor of two integers is 1, the integers are said to be coprime.

So how can we find the greatest common factor?

There are a number of different ways to do this, but our worksheets use two of the most common:

• listing all the factors method
• prime factorization method

If you want to learn more about the Greatest Common Factor and how each of the methods above works, come and visit our Definition of Greatest Common Factor page.

We have lots of worked examples showing you how to find the greatest common factor using different methods.

Our Greatest Common Factor calculator will tell you the highest common factor between 2 or more numbers.

It will also list the factors of each of the numbers and tell you whether they are coprime or not.

We have split our Greatest Common Factor worksheets into two main sections: the A group and the B group.

The A group uses the listing all the factors of both numbers to find the greatest common factor.

The B group uses the prime factorization method to find the greatest common factor.

The A and B sheets are supported sheets and provide a framework for finding the gcf.

In the third section, there are also harder sheets for more advanced students which can be used with either method.

In our final worksheet section, we have some combined Greatest Common Factor and Lowest Common Multiple worksheets.

This section is for students who are already proficient at finding the GCF and do not need any extra support or prompts.

The Least Common Multiple and Greatest Common Factor are often taught alongside each other.

These sheets involve finding both the LCM and GCF on the same sheet.

The first two sheets are easier and keep the numbers for the LCM and GCF separate.

The third and fourth sheets involve finding the LCM and GCF of the same numbers.

The fourth sheet involves 3 numbers rather than 2.

This short video walkthrough shows several problems from our GCF and LCM 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 these sheets, check out the video!

Looking for something a little different to get children to apply their knowledge of GCF and LCM?

Using riddles is a great way to explore and apply your LCM and GCF knowledge by solving problems.

The aim is to find the correct answer out of 6 choices from following the clues.

There are 2 riddles on each sheet.

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

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

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.

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

Our Greatest Common Factor calculator will tell you the highest common factor between 2 or more numbers.

It will also list the factors of each of the numbers and tell you whether they are coprime or not.

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.

Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.

It will also show you the working out using a choice of two different methods.

There are also some worked examples on the page with explanation of how it works.

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!

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.