GCF / GCD Calculator
Find the Greatest Common Factor (GCF) — also called GCD — of two or more numbers, with Euclidean algorithm steps and prime factorisation shown.
What Does This Tool Do?
Find the Greatest Common Factor (GCF) — also called Greatest Common Divisor (GCD) — of two or more numbers, with Euclidean algorithm steps and prime factorisation both shown.
Key Features
Multiple Numbers
GCF of 2 or more integers at once.
Euclidean Steps
Division-based GCD algorithm shown.
Prime Factors
Factorisation of each input shown.
Instant
Results immediately.
How to Use
- Enter 2 or more positive integers separated by commas or spaces.
- Click Calculate GCF.
- Read the result, Euclidean steps and prime factorisation.
Frequently Asked Questions
What is GCF?▾
The Greatest Common Factor (also GCD — Greatest Common Divisor) is the largest number that divides all the given integers without remainder. E.g. GCF(48, 36) = 12.
What is GCF used for?▾
Simplifying fractions (divide numerator and denominator by their GCF), factoring algebraic expressions, and number theory.
What is the Euclidean algorithm?▾
GCD(a, b) = GCD(b, a mod b), repeated until the remainder is 0. It is the most efficient algorithm for computing GCD, developed in ancient Greece.