GCF Calculator
Free online GCF calculator to find the greatest common factor of two or more numbers. Calculate GCF with step-by-step explanation and examples.
How to Calculate GCF?
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. It's useful for simplifying fractions and solving various mathematical problems.
Finding GCF of Multiple Numbers:
- Find the GCF of the first two numbers
- Use that result to find the GCF with the next number
- Continue until all numbers are processed
GCF(12, 18, 24) = 6
Finding GCF using Prime Factorization:
- Find the prime factors of each number
- Identify the common prime factors
- Multiply the common prime factors with the lowest exponents
48 = 2⁴ × 3
60 = 2² × 3 × 5
GCF(48, 60) = 2² × 3 = 12
Common GCF examples
| Numbers | GCF |
|---|---|
| 12, 18 | 6 |
| 24, 36 | 12 |
| 15, 25 | 5 |
| 8, 12, 16 | 4 |
| 20, 30, 40 | 10 |
| 7, 11 | 1 |
| 100, 200 | 100 |