What is a greatest common factor?

The greatest common factor (GCF), also called the highest common factor, is the biggest whole number that is a factor of every number in a set. You find it by listing each number's factors and picking the largest they share. It is the key to simplifying fractions.

Examples

• Factors of 12: 1, 2, 3, 4, 6, 12; factors of 18: 1, 2, 3, 6, 9, 18; the GCF is 6.
• The GCF of 8 and 12 is 4.
• The GCF of 5 and 9 is 1 (they share no other factor).

Quick facts

• Dividing a fraction's top and bottom by their GCF gives its simplest form.
• If two numbers share only 1, they are called co-prime.