GCF Calculator — Greatest Common Factor (GCD / HCF)

Reviewed August 7, 2026

ResultUpdates as you type

Greatest Common Factor (GCF)12

Count of Numbers3

Find the Greatest Common Factor (GCF, GCD, HCF) of two or more numbers instantly using the Euclidean algorithm and prime factorization.

Find the Greatest Common Factor (GCF), Greatest Common Divisor (GCD), or Highest Common Factor (HCF) of a set of numbers.

Understanding Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest positive integer that divides each of the numbers in a given set without leaving a remainder. It is widely used in simplifying fractions, algebraic factoring, and number theory problems.

Methods for Finding GCF

Euclidean Algorithm: An efficient division algorithm based on the principle that the greatest common divisor of two numbers also divides their difference.
Prime Factorization: Expressing each number as a product of primes and multiplying the smallest powers of common prime factors.

How to use

Enter two or more positive integers separated by commas, spaces, or lines.
The calculator computes the Greatest Common Factor using Euclidean division.
View the resulting GCF value.

Formula

Euclidean Algorithmgcd(a, b) = gcd(b, a mod b)Repeated division until remainder becomes zero.

Prime Factorization MethodGCF = product of lowest powers of common prime factorsMultiply common prime factors elevated to their minimum exponent.

Worked examples

Finding GCF of 24, 36, and 48

Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 48: 1,2,3,4,6,8,12,16,24,48. GCF = 12.

Frequently asked questions

What is GCF?

The GCF (Greatest Common Factor), also called GCD (Greatest Common Divisor) or HCF (Highest Common Factor), is the largest integer that divides two or more numbers without leaving a remainder.

What is the relationship between GCF and LCM?

For any two positive integers a and b: GCF(a, b) × LCM(a, b) = a × b.