Finding the Greatest Common Factor

The greatest common factor of two or more whole numbers is the largest whole number that divides evenly into each of the numbers. There are two ways to find the greatest common factor.

The first method is to list all of the factors of each number, then list the common factors and choose the largest one.

Find the GCF of 36 and 54.


The factors of 36 are

1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 54 are

1, 2, 3, 6, 9, 18, 27, and 54.

The common factors of 36 and 54 are

1, 2, 3, 6, 9, 18

Although the numbers in bold are all common factors of both 36 and 54, 18 is the greatest common factor.

GARD Pro Not Registered
The second method to find the greatest common factor is to list the prime factors, then multiply the common prime factors.

Let’s use the same numbers, 36 and 54 again to find their greatest common factor.


The prime factorization of 36 is

2 x 2 x 3 x 3

The prime factorization of 54 is

2 x 3 x 3 x 3

Notice that the prime factorizations of 36 and 54 both have one 2 and two 3s in common. So, we simply multiply these common prime factors to find the greatest common factor. Like this…

2 x 3 x 3 = 18

Both methods for finding the greatest common factor work!

GARD Pro Not Registered


Homework Helpers

These great tips will really simplify your fractions homework. Click here >

How to Do Fractions

Tutorials on how to add, subtract, multiply and divide fractions! Click here to start with adding >

Fraction Calculator

Learn how to solve fraction problems, then check your work with our online fraction calculator. Click here >

Fraction Worksheets

Free downloadable worksheets give you tons of practice to learn how to solve fraction problems. Click here >

Further examples of greatest common factor.