Greatest Common Factor Calculator
Find the GCF (Greatest Common Factor, also known as GCD) of two or more integers — the largest number that divides all of them evenly.
How to use the Greatest Common Factor Calculator
- Enter your inputs into the Greatest Common Factor Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The Euclidean algorithm
GCD(a, b) = GCD(b, a mod b), repeat until remainder = 0
Highly efficient: divide larger by smaller, replace pair with (divisor, remainder), repeat. Terminates quickly even for very large numbers.
Worked example
GCD(48, 18): 48 mod 18 = 12 → GCD(18, 12); 18 mod 12 = 6 → GCD(12, 6); 12 mod 6 = 0 → GCD = 6. GCD of 24, 36, 60: GCD(24,36)=12; GCD(12,60)=12.
Frequently asked questions
When do I use GCF?
Simplifying fractions (divide numerator and denominator by GCF), reducing ratios, factoring polynomials, cryptography (RSA uses related concepts), partitioning into equal groups.
What if GCD equals 1?
The numbers are "coprime" or "relatively prime" — they share no common factors other than 1. Important in number theory and cryptography.
How does this relate to LCM?
For two numbers: GCF × LCM = product of the two numbers. Knowing one tells you the other given the product.