How is GCF calculated?

The most efficient method is the Euclidean algorithm: repeatedly divide the larger number by the smaller and replace with the remainder until the remainder is 0. The last non-zero remainder is the GCF.

What is the difference between GCF and LCM?

GCF is the largest shared factor; LCM is the smallest shared multiple. GCF(12,8)=4; LCM(12,8)=24. Relationship: GCF × LCM = a × b.

GCF is used to simplify fractions (divide numerator and denominator by GCF), simplify ratios, solve tile/division problems, and as a building block for calculating LCM.

GCF Calculator — Greatest Common Factor

The GCF Calculator finds the Greatest Common Factor (GCF) — also called the Greatest Common Divisor (GCD) — of two numbers. The GCF is the largest number that divides both values without a remainder. It is used to simplify fractions, find LCM, and solve problems in algebra and number theory.

First Number

Second Number

How to Use This Calculator

1
Enter the first number.
2
Enter the second number.
3
Click Calculate to find the Greatest Common Factor.

Frequently Asked Questions

The Greatest Common Factor (GCF) of two numbers is the largest number that divides both of them without a remainder. GCF(48, 36) = 12, since 12 is the largest number dividing both 48 and 36.

Related Calculators

🧮LCM Calculator 🧮Fraction Calculator 🧮Prime Factor Calculator