Free Greatest Common Factor (GCF) Calculator

Find the greatest common factor (GCF) of two numbers. Also known as the greatest common divisor (GCD) or highest common factor (HCF).

Gcf

12

Lcm Val144
Product1,728

How to Find the Greatest Common Factor

Methods

Method 1: Prime Factorization 1. Find the prime factors of each number 2. Identify the common prime factors 3. Multiply the common factors together

Method 2: Euclidean Algorithm 1. Divide the larger number by the smaller 2. Replace the larger number with the remainder 3. Repeat until the remainder is 0 4. The last non-zero remainder is the GCF

Useful Identity

GCF(a, b) × LCM(a, b) = a × b

Example Calculation

Find the GCF of 48 and 36.

  1. 01Prime factorization of 48: 2⁴ × 3 = 2 × 2 × 2 × 2 × 3
  2. 02Prime factorization of 36: 2² × 3² = 2 × 2 × 3 × 3
  3. 03Common factors: 2² × 3 = 4 × 3
  4. 04GCF(48, 36) = 12

Frequently Asked Questions

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