GCF Calculator

Free GCF calculator: enter two whole numbers to find their greatest common factor instantly using the Euclidean algorithm - with steps shown.

First Number

Second Number

About this tool

The greatest common factor is the largest number that divides two numbers evenly - the key that unlocks fraction simplification. The GCF of 48 and 180 is 12, which is why 48/180 reduces cleanly to 4/15.

Instead of listing every factor by hand, this calculator uses the Euclidean algorithm: an ancient, lightning-fast method that repeatedly replaces the larger number with the remainder of dividing by the smaller one. Two thousand years old, still the best way.

How to use

Enter two whole numbers (1 or larger) and press Find GCF.

You get the greatest common factor immediately, plus a bonus: the fraction a/b reduced to lowest terms using that factor. Students can use it to check homework; everyone else can use it to simplify ratios, recipes, and proportions.

The math behind it

Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), repeating until the remainder is 0 - the last non-zero remainder is the GCF. Example: GCF(48, 180) -> GCF(180, 48) -> GCF(48, 36) -> GCF(36, 12) -> GCF(12, 0) = 12.

Once you have the GCF, dividing both numbers by it gives the simplest form of any fraction or ratio built from them.

Frequently asked questions

What is the difference between GCF and GCD?

Nothing - GCF (greatest common factor) and GCD (greatest common divisor) are two names for the same thing. Mathematicians tend to say GCD; schools usually teach GCF.

What is the GCF used for in real life?

Simplifying fractions, reducing ratios (a 48:180 recipe becomes 4:15), splitting items into equal groups, and sizing tiles or patterns that must divide a space evenly.

What if the two numbers share no factors?

Then the GCF is 1, and the numbers are called coprime - like 8 and 15. The fraction is already in lowest terms and cannot be simplified.

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