Find the Greatest Common Factor (GCF/HCF) of two or more numbers. Free online GCF calculator.
| Numbers | — |
| GCF / HCF | — |
| Factors of GCF | — |
The Greatest Common Factor (GCF), also called HCF (Highest Common Factor) or GCD (Greatest Common Divisor), is the largest number that divides two or more given numbers exactly without a remainder. GCF is used to simplify fractions, split items into equal groups, and solve ratio problems.
Methods to find GCF:
1. Prime Factorization: Find primes of each number, take the lowest power of common primes, multiply.
2. Euclidean Algorithm: Divide larger by smaller, replace larger with remainder, repeat until remainder = 0. Last divisor = GCF.
3. Listing Factors: List all factors of each number, find the largest common one.
| Numbers | GCF/HCF | Prime Factorization |
|---|---|---|
| 12, 18 | 6 | 12=2²×3, 18=2×3² → GCF=2×3=6 |
| 24, 36 | 12 | 24=2³×3, 36=2²×3² → GCF=2²×3=12 |
| 7, 13 | 1 | Co-prime numbers — GCF always 1 |
| 48, 64, 80 | 16 | Common factor: 16 |
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