What Is the Greatest Common Factor (GCF)?
The Greatest Common Factor (also called Greatest Common Divisor, or GCD) is the largest number that divides evenly into all the numbers in a set. It's used for simplifying fractions and solving various number theory problems.
How to Use the GCF Calculator
- Enter two or more numbers, separated by commas.
- View the greatest common factor instantly.
How GCF Is Calculated
This calculator uses the Euclidean algorithm, an efficient method that repeatedly divides and takes remainders until reaching zero — much faster than listing all factors for large numbers.
Worked Example
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Greatest common factor: 12
Common Uses for GCF
- Simplifying fractions to their lowest terms.
- Solving word problems involving equal grouping or distribution.
- Factoring algebraic expressions.
Common Mistakes to Avoid
- Confusing GCF (largest shared factor) with LCM (smallest shared multiple) — they answer opposite questions.
- Listing factors manually for large numbers instead of using the more efficient Euclidean algorithm.
Frequently Asked Questions
It's the largest number that divides evenly into every number in a given set, with no remainder.
The Euclidean algorithm is an efficient method: repeatedly divide the larger number by the smaller, replacing the larger with the remainder, until the remainder is 0 — the last non-zero remainder is the GCF.
GCF (Greatest Common Factor) is the largest number that divides into all given numbers. LCM (Least Common Multiple) is the smallest number that all given numbers divide into — they're related but different concepts.
Divide both the numerator and denominator by their GCF to reduce a fraction to its lowest terms.
Yes — this calculator supports finding the GCF across any number of values by finding the GCF of the first two, then the GCF of that result with the next number, and so on.