How the gcf calculator works
This calculator uses the Euclidean algorithm, which repeatedly applies the fact that GCF(a, b) equals GCF(b, a mod b), until the remainder reaches zero:
GCF(a, b) = GCF(b, a mod b), until b = 0
then GCF = a
then GCF = a
For more than two numbers, the GCF is computed pairwise across the whole list.
Step-by-step guide
- Enter two or more whole numbers, separated by commas.
- Read the Greatest Common Factor instantly.
Worked example
For 24, 36 and 60: the Euclidean algorithm gives GCF(24,36) = 12, then GCF(12,60) = 12 — so 12 is the largest number that divides all three evenly.
Frequently asked questions
GCF is commonly used to simplify fractions to their lowest terms, and to solve problems that involve splitting items into equal groups.
Yes — Greatest Common Factor (GCF) and Highest Common Factor (HCF) are the same concept, just different regional naming conventions.
That's a valid result — it means the numbers are 'coprime,' and the GCF will simply be 1.