A Greatest Common Factor (GCF) calculator, also called Greatest Common Divisor (GCD), finds the largest positive integer that divides both input numbers evenly.
About this calculator
A Greatest Common Factor (GCF) calculator, also called Greatest Common Divisor (GCD), finds the largest positive integer that divides both input numbers evenly. GCF is used to simplify fractions, solve LCM problems, and in number theory.
The Euclidean algorithm efficiently finds GCF: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is 0.
Common uses
- Simplify fractions by dividing by the GCF
- Divide items into equal groups without leftovers
- Solve problems requiring equal division
- Find common factors in algebraic expressions
Frequently asked questions
What is the GCF of 36 and 48?
Using the Euclidean algorithm: GCF(48, 36) → GCF(36, 12) → GCF(12, 0) = 12. So GCF(36, 48) = 12. This means 12 is the largest number that divides both 36 (36÷12=3) and 48 (48÷12=4) without a remainder.