Greatest Common Factor and the Distributive Property Worksheet 

So what exactly does GCF mean? The greatest common factor (GCF) is the largest positive integer that divides two or more integers without leaving a remainder. It can be found by listing the factors of each number and finding the greatest number that they have in common. For example, the GCF of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

The distributive property is a property of arithmetic that allows you to multiply a single term by the sum or difference of two or more other terms. It states that:

a(b + c) = ab + ac

Let’s take a look at how these concepts work together with 16 + 32. To express this using the distributive property, you would first have to find the GCF of 16 and 32. This equals to be 16. We can then rewrite the equation as 16(1+2) using the distributive property.

There are 3 worksheets included with this download. These worksheets focus on finding the greatest common factor and using the GCF and distributive property to express the sum as a product.

An answer key is included with your download to make grading fast and easy! 

Tips for Differentiation + Scaffolding 

In addition to independent student work time, use this worksheet as an activity for:

• Guided math groups 
• Lesson warm-up
• Lesson wrap-up
• Fast finishers 
• Homework assignment
• Whole-class review (via smartboard)

Students that require extension can create their own word problems to share with classmates. 

Students that need scaffolding could use a personal whiteboard or blank paper to have more visual space to show their working out. They can use the GCF poster as a reference to assist with each step.

🖨️ Easily Download & Print

Use the dropdown icon on the Download button to choose between the PDF or editable Google Slides version of this resource. 

Because this resource includes an answer sheet, we recommend you print one copy of the entire file. Then, make photocopies of the blank worksheet for students to complete. 

Turn this teaching resource into a sustainable activity by printing on cardstock and slipping it into a dry-erase sleeve. Students can record their answers with a whiteboard marker, then erase and reuse them. 

Additionally, project the worksheet onto a screen and work through it as a class by having students record their answers in their notebooks.

Get more worksheets to have handy!

This resource was created by Jillian Sloane, a teacher in West Virginia and a Teach Starter Collaborator. 

Don’t stop there! We’ve got more activities to shorten your lesson planning time: 

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Greatest Common Factor – Task Cards

Practice how to find the greatest common factor (GCF) with this set of 24 task cards.

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Greatest Common Factor Doodle Notes

Learn how to find the GCF with this set of doodle notes.

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Greatest Common Factor – Mini Book

Learn different strategies to find the greatest common factor with this mini-book.