GCF: Common Factors and The Greatest Common Factor

Common Factors

Let us say you have worked out the factors of two or more numbers:

Common Factors of 12 and 30

Factors of 12: 1, 2, 3, 4, 6 and 12

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

The common factors are those that are found in both lists: 1, 2, 3, and 6

It is a common factor when it is a factor of two or more numbers.
(It is then "common to" those numbers.)

Greatest Common Factor: GCF

The GCF is the largest common factor of two or more numbers. 

In the example above, 6 is the GCF because it is the largest factor.

Greatest Common Factor of 12 and 30

Factors of 12: 1, 2, 3, 4, 6 and 12

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

GCF of more than two numbers

Here is another example with three numbers:

Greatest Common Factor of 15, 30 and 105

Factors of 15 are 1, 3, 5, and 15

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105

The factors that are common to all three numbers are 1, 3, 5 and 15

The Greatest Common Factor is 15. 

When do we use this?

Being able to find the GCF is an important skill. We can use the GCF when we are putting a fraction into lowest terms.

Even though 2, 4, and 8 are all common factors, 8 is the GCF and helps you reduce quicker.

Important Note: Greatest Common Factor is sometimes called the Greatest Common Divisor.