GCF Calculator

About the GCF Calculator

The Greatest Common Factor (GCF) — also called Greatest Common Divisor (GCD) or Highest Common Factor (HCF) — is the largest positive integer that divides two or more numbers without a remainder. The GCF is essential for simplifying fractions, solving algebraic equations, and understanding number theory. Our calculator uses the highly efficient Euclidean algorithm and shows the prime factorisation method as a learning tool.

How It Works

The Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), repeating until the remainder is 0. The last non-zero remainder is the GCF. For GCF(48, 36): 48 = 1×36 + 12 → GCF(36, 12). 36 = 3×12 + 0 → GCF = 12. Alternative: prime factorisation method — factor each number and multiply shared prime factors: 48 = 2⁴×3, 36 = 2²×3² → GCF = 2²×3 = 12.

Tips & Best Practices

• ✓GCF is used to reduce fractions to lowest terms: 24/36 → divide by GCF(24,36) = 12 → 2/3.
• ✓Two numbers whose GCF = 1 are called coprime or relatively prime (e.g., 8 and 9).
• ✓GCF × LCM = product of the two numbers: GCF(12,18) × LCM(12,18) = 12 × 18 = 216.
• ✓In algebra, factoring expressions uses GCF: 12x² + 8x = 4x(3x + 2), where 4x is the GCF.
• ✓The GCF of consecutive integers is always 1 (e.g., GCF(7,8) = 1).

Who Uses This Calculator

Students simplifying fractions, algebra learners factoring expressions, programmers optimising algorithms that work with ratios, architects designing grids with equal spacing, and number theory enthusiasts exploring divisibility all use GCF calculations.