Greatest Common Factor

The greatest common factor (GCF) of two numbers is the largest number or factor that can evenly divide the two given numbers.

For example, let’s find the GCF of 60 and 72.

The first step is to list ALL the factors of each number.

• Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
• Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Now that we have all the factors of both numbers, we need to find the factor that is common to both 60 and 72, however, it must be the largest or the number that has the highest value.

You may notice that the math word – Greatest Common Factor – is self-explanatory. This is because we are literally trying to identify the common factor of two numbers with the greatest value.

So if we compare all the factors of both 60 and 72, the greatest common factor is the number 12.

We can also express this as GCF\left( {60,72} \right) = 12.