GCF Calculator
Find the Greatest Common Factor (GCF) of two integers with step-by-step division.
What is GCF (Greatest Common Factor)?
The Greatest Common Factor (GCF) is the largest positive integer that divides two or more integers without leaving a remainder. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Their common factors are 1, 2, 3, 4, 6, 12, so GCF(24, 36) = 12.
GCF is also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF). Finding the GCF is crucial for simplifying fractions, finding common denominators, and solving real-world sharing or grouping problems.
GCF Step-by-Step Calculator
See how the Euclidean algorithm solves GCF. Watch the divisions step-by-step.
Euclidean Steps
| Step | Equation | Remainder |
|---|---|---|
| 1 | 60 = 48 × 1 + 12 | 12 |
| 2 | 48 = 12 × 4 + 0 | 0 |
Examples of Greatest Common Factor
Learn how different methods work on common number pairs.
24 = 2³ × 3, 36 = 2² × 3². Shared primes at lowest exponents: 2² × 3 = 12.