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

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