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