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How to find the greatest common factor (GCF)

The Greatest Common Factor (GCF) is the largest positive integer that is a factor of two or more numbers. Look at the examples below to see how to find the Greatest Common Factor.

What is the Greatest Common Factor of 16 and 20?

Here is another example of finding the Greatest Common Factor

What is the Greatest Common Factor of 12 and 42?

Solving problems using the Greatest Common Factor

The example below shows how we can use GCF to solve problems.

Problem: We have three containers. One contains 12 liters of milk, one contains 15 liters of juice and the other 24 liters of water.

We want to empty each container into bottles. The bottles must all be filled and must be the same size.

What is the largest size that the bottles can be?

We need to find the Greatest Common Factor of 12 , 15 , and 24 because that number will be the largest size that the bottles can be.