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GCF using Euclidean Algorithm

Free printable and online worksheets to help Grade 6 students learn how to use the Euclidean Algorithm to find the GCF or the GCD.

The Euclidean Algorithm is an efficient method for finding the Greatest Common Factor (GCF) of two whole numbers.

Here’s how it works:

- Divide the larger of the two numbers by the smaller one.
- If there is a remainder, divide it into the divisor.
- Continue dividing the last divisor by the last remainder until the remainder is zero.
- The final divisor is the GCF of the original pair of numbers.

In application, the algorithm can be used to find the side length of the largest square that can be used to completely fill a rectangle without overlap or gaps.

Have a look at this video if you need to review how to use the Euclidean Algorithm to find the GCF or GCD.

Click on the following worksheet to get a printable pdf document.

Scroll down the page for more **GCF using Euclidean Algorithm Worksheets**.

**Printable**

(Answers on the second page.)

GCF using Euclidean Algorithm Worksheet #1

GCF using Euclidean Algorithm Worksheet #2

GCF using Euclidean Algorithm Worksheet #3

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