Daily Figures Edition No Sign-Up • No Tracking • Free Forever Vol. XII — No. 204
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Math — Number Theory

GCF Calculator

Enter two numbers to get the greatest common factor — and the least common multiple.

Filed by The Statistics Desk  |  Method: Euclidean algorithm
Greatest common factor
—
Largest number dividing both.
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Least common multiple—
First number—
Second number—
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Enter your figures above to see the step-by-step working.
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How the GCF Calculator Works

The greatest common factor (GCF), also called the greatest common divisor, is the largest whole number that divides two numbers evenly. It is what you use to reduce fractions to lowest terms and to simplify ratios. This calculator finds it using the Euclidean algorithm, which repeatedly replaces the larger number with its remainder until nothing is left over.

As a bonus it also shows the least common multiple (LCM), since the two are linked: the product of two numbers equals their GCF times their LCM. Enter two positive whole numbers to see both.

GCF × LCM = a × b

Frequently Asked Questions

What is the greatest common factor?

It is the largest whole number that divides both of your numbers with no remainder. For 12 and 18 it is 6, since 6 is the biggest number that goes into both.

How is the GCF used?

It reduces fractions to lowest terms — divide the numerator and denominator by their GCF — and simplifies ratios and many algebra problems.

How does the calculator find it so fast?

It uses the Euclidean algorithm: divide the larger number by the smaller, keep the remainder, and repeat. The last non-zero remainder is the GCF.

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