# Greatest Common Factor (GCF)

This tutorial will explain what the greatest common factor (GCF) is and how to find it.

## Factors

Numbers that are multiplied together to get another number.

Example: All the factors of 36.

• 1 x 36 = 36
• 2 x 18 = 36
• 3 x 12 = 36
• 4 x 9 = 36
• 6 x 6 = 36

Therefore the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

In addition, the opposites of these whole numbers would be factors as well since -4 x -9 = 36.

So, all the factors of 36 are -36, -18, -12, -9, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 9, 12, 18, and 36.

To simplify fractions, we usually only need to know the positive factors.

## Common Factors

The factors that are shared by tow numbers.

For example: 12 and 18.

Factors of 12 are 1, 2, 3, 4, 6, and 12.

Factors of 18 are 1, 2, 3, 6, 9, and 18.

The common factors for both numbers are 1, 2, 3, and 6.

## Greatest Common Factor

The greatest common factor (GCF) is the “largest” common factor of two or more numbers.

From the previous example, the greatest common factor of 12 and 18 is 6, because the largest same factor of 12 and 18 is 6.

There are two popular methods for finding GCF: make a list or prime factorization.

## Watch a Video Tutorial

Here is a video tutorial comparing fractions.

## Interactive Class on this Topic

Take an interactive middle school math class on this material, click here