GCF Calculator

The greatest common factor (GCF) of two or more whole numbers is the largest number that divides every one of them with no remainder. It is also called the greatest common divisor (GCD) or highest common factor (HCF). For 48 and 60, the GCF is 12, because 12 divides both 48 and 60 evenly and no larger number does.

The fastest method is the Euclidean algorithm: replace the pair (a, b) with (b, a mod b) repeatedly until the second number becomes 0. The first number at that point is the GCF. For three or more numbers, fold the algorithm: gcf(a, b, c) = gcf(gcf(a, b), c). This calculator uses that approach and shows the steps.

GCF is the largest number that divides all inputs; LCM is the smallest number that all inputs divide into. For 4 and 6: GCF is 2 (largest divisor of both), LCM is 12 (smallest multiple of both). They are connected by the rule lcm(a, b) = (a × b) ÷ gcf(a, b).

Simplifying fractions (divide numerator and denominator by their GCF to reduce to lowest terms), splitting items into equal groups, and number-theory problems. The GCF tells you the size of the largest evenly-shared piece.

Yes. Separate the numbers with commas or spaces, for example '48, 60, 84'. The calculator folds the Euclidean algorithm across the full list.

By convention gcd(n, 0) = n for any positive n, but in everyday math GCF is computed for positive whole numbers. This calculator requires every input to be a positive whole number to avoid confusing edge cases.