GCF calculator
The greatest common factor (GCF or GCD) of two or more numbers.
About this calculator
This GCF calculator finds the greatest common factor of a list of whole numbers: the largest number that divides all of them exactly.
It's also called the greatest common divisor (GCD) or highest common factor (HCF), and it's what you use to simplify fractions.
How it works
Uses Euclid’s method: repeatedly replace the larger number with the remainder after dividing it by the smaller, until the remainder is 0. The last non-zero number is the GCF. Prime factors are shown for each number.
Last reviewed:
Worked example
- Whole numbers, separated by spaces or commas: 48, 180, 60
Greatest common factor: 12
Common questions
How do I find the GCF of two numbers?
List the prime factors of each and multiply the ones they share. For 48 = 2⁴ × 3 and 180 = 2² × 3² × 5, the shared part is 2² × 3 = 12.
What is the GCF used for?
Simplifying fractions and ratios. Dividing 48/180 top and bottom by 12 gives 4/15.
What if the GCF is 1?
Then the numbers have no common factor besides 1, and are called coprime.
The story behind it
Where the idea came from: Euclid described his method for the greatest common divisor in his Elements around 300 BC. It is one of the oldest algorithms still in use.
Euclid's algorithm needs only division and remainders, and it is so efficient that computers still use it, for example in the cryptography that secures websites.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
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