Finding the Greatest Common Factor in Algebra
(KS3, Year 7)

The Lesson

The greatest common factor of two or more terms in algebra can be found. Imagine we wanted to find the greatest common factor of the two terms shown below:

2 x squared y squared and 4 x y cubed

How to Find the Greatest Common Factor in Algebra

Finding the greatest common factor in algebra is easy.

Question

What is the greatest common factor of the terms shown below?
2 x squared y squared and 4 x y cubed

Step-by-Step:

1

Look at the number that appears in both terms.
2 x2y2, 4 xy3
Find the greatest common factor of these numbers. In our example, the greatest common factor of 2 and 4 is 2.

2 Read more about finding the greatest common factor of a number

2

Look at the letters (and/or brackets) that appear in both terms. In our example, x and y appear in both terms. For each letter that appears in both terms, find the letter with the smallest exponent.
  • Look at the x terms.
    2 x2 y2, 4 x y3
    x has the smallest exponent. (x has an implicit exponent of 1 (x = x1), whereas x2 has an exponent of 2).

    x
  • Look at the y terms.
    2x2 y2 , 4x y3
    y2 has the smallest exponent. (y2 has an exponent of 2, whereas y3 has an exponent of 3).

    y squared

3

Write the terms found in the previous Steps next to each other.

Answer:

The greatest common factor of 2x2y2 and 4xy3 is:

2 x y squared

Lesson Slides

The slider below gives another example of finding the greatest common factor in algebra, and some examples of why it is useful. Open the slider in a new tab

What Is a Factor in Algebra?

A factor is a quantity that divides exactly into a term. A factor is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term.

What Is the Greatest Common Factor in Algebra?

The greatest common factor in algebra is the largest factor that is common to two or more terms.

Finding the Greatest Common Factor of More Than Two Terms

In the examples here, the greatest common factor has been been found for two terms. But the same procedure extends to any number of terms.
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See Also

What is algebra? What is the greatest common factor in algebra? What is a factor in algebra? What is the greatest common factor? Finding the greatest common factor What is an exponent?