The Greatest Common Factor (GCF) is the largest positive integer that divides all given numbers without a remainder.

What is the difference between GCF and LCM?

GCF is the largest shared factor; LCM is the smallest common multiple. GCF × LCM = a × b for two numbers.

How is GCF used in fractions?

Divide numerator and denominator by their GCF to simplify. 12/16 → GCF = 4 → 3/4.

GCF Calculator

Enter two or more positive integers separated by commas to find their Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), along with all common factors.

How to use this calculator

Enter two or more positive integers, separated by commas or spaces.
Read the GCF and the complete list of all common factors.

Formula & method

Euclidean algorithm

GCF(a, b) = GCF(b, a mod b) — repeat until remainder = 0

For more than two numbers, compute GCF(GCF(a, b), c), etc. Common factors are all divisors of the GCF.

Example

GCF(24, 36, 60): GCF(24,36) = 12, GCF(12,60) = 12. Common factors of GCF = 12: 1, 2, 3, 4, 6, 12.

Key insights

The GCF of two prime numbers is always 1 — primes share no common factors other than 1.
The Euclidean algorithm is highly efficient: GCF(a, b) = GCF(b, a mod b), repeating until b = 0.
GCF is used to simplify fractions to lowest terms: 12/16 = 3/4 (divided by GCF = 4).
GCF × LCM = a × b for any two integers a and b.

How to interpret your result

GCF vs common factors

Common factors are all integers dividing all inputs. The GCF is the largest of those common factors.

GCF = 1 (coprime)

If GCF = 1, the numbers are coprime — they share no common factor other than 1. For example, GCF(8, 15) = 1.

Frequently asked questions

What is the GCF?: The Greatest Common Factor (GCF) is the largest positive integer that divides all given numbers without a remainder.
What is the difference between GCF and LCM?: GCF is the largest shared factor; LCM is the smallest common multiple. GCF × LCM = a × b for two numbers.
How is GCF used in fractions?: Divide numerator and denominator by their GCF to simplify. 12/16 → GCF = 4 → 3/4.

Related calculators

LCM Calculator — Find the Least Common Multiple (LCM) of two or more integers to solve fraction addition and scheduling problems.
Factor Calculator — Find all factors, factor pairs, prime factorization, and check if a number is prime for any positive integer.
Fraction Calculator — Add, subtract, multiply, and divide fractions with step-by-step simplification and mixed number conversions.

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