GCF Calculator

Find the Greatest Common Factor of two or more numbers using the Euclidean algorithm.

GCF & LCM Calculator

GCF / HCF / GCD

6

Greatest Common Factor

LCM

72

Least Common Multiple

GCF × LCM = 6 × 72 = 432

GCF Calculator Formula & How It Works

GCF(a,b) = GCF(b, a mod b) (Euclidean Algorithm)
  • Euclidean algorithm: repeatedly apply GCF(a,b) = GCF(b, a mod b)
  • Base case: GCF(a, 0) = a
  • Multiple numbers: GCF(a,b,c) = GCF(GCF(a,b), c)
  • Equivalent names: GCD (Greatest Common Divisor), HCF (Highest Common Factor)

The GCF of two numbers is the largest integer that divides both without remainder. The Euclidean algorithm finds it efficiently: GCF(48,18) → GCF(18,12) → GCF(12,6) → GCF(6,0) = 6. GCF is used to simplify fractions, find common denominators, and solve Diophantine equations.

GCF Calculator FAQs

How do you find the GCF of two numbers?

Method 1 (Euclidean): GCF(a,b) = GCF(b, a mod b) until b=0. Method 2 (prime factors): list all prime factors of each, multiply common ones. GCF(12,8): 12=2²×3, 8=2³ → common factor = 2² = 4.

What is GCF used for?

Simplifying fractions (divide numerator and denominator by GCF), finding common denominators (through LCM = a×b/GCF), tile/packaging problems (finding largest equal groups), and cryptography.

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