How to Find the Greatest Common Factor (GCF): 3 Easy Methods (2026)

The greatest common factor (GCF) is the largest whole number that divides two or more numbers with no remainder. There are three classic ways to find it — listing factors, prime factorization, and the Euclidean algorithm — and this guide shows all three with worked examples.

Try any of them instantly in the GCD / GCF Calculator, which shows every step.

GCF, GCD and HCF are the same

Greatest common factor, greatest common divisor and highest common factor are three names for one idea: the biggest number dividing all your inputs evenly.

Method 1: List the factors

Write every factor of each number and pick the largest they share. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest shared factor is 12. Great for small numbers; use the Factors Calculator to list them, or the standalone GCF calculator at gcfcalculator.xyz to compare the shared factors of two or more numbers side by side.

Method 2: Prime factorization

Factor each number into primes and multiply the lowest power of each shared prime. 24 = 2³ × 3 and 36 = 2² × 3²; the shared primes give 2² × 3 = 12. See prime factorization for the breakdown.

Method 3: Euclidean algorithm

Replace the larger number with its remainder when divided by the smaller, and repeat until the remainder is 0. gcd(36, 24) → gcd(24, 12) → gcd(12, 0) = 12. This is the fastest method for big numbers — see the Euclidean algorithm guide.

Which method to choose

• Small numbers: list factors.
• Want primes/LCM too: prime factorization.
• Large numbers: the Euclidean algorithm.

Remember the link GCF × LCM = a × b, so you can get the LCM for free.