Greatest Common Factor Calculator
Find the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) for a list of numbers. See the prime factorization steps and all common factors instantly.
Separate numbers with commas or spaces.
What is the Greatest Common Factor?
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest positive integer that divides evenly into two or more numbers without leaving a remainder.
For example, for the numbers 12 and 18:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common Factors: 1, 2, 3, 6
- GCF: 6
Methods to Find GCF
1. Prime Factorization
Break each number down into its prime number building blocks. The GCF is the product of all common prime factors.
- 24 = 2 × 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
- Common primes: 2, 2, 3
- GCF = 2 × 2 × 3 = 12
2. Euclidean Algorithm
This is an efficient method used by calculators (including this one). To find the GCD of two numbers, you subtract the smaller number from the larger one (or use the modulus operator) until one becomes zero. The remaining non-zero number is the GCD.
? Frequently Asked Questions
Yes! Greatest Common Divisor (GCD), Highest Common Factor (HCF), and Greatest Common Factor (GCF) all refer to the exact same mathematical concept.
Yes. If the numbers share no common factors other than 1 (like 8 and 15), the GCF is 1. These numbers are called 'relatively prime' or 'coprime'.
It is most commonly used to simplify fractions. For example, to simplify 12/18, you divide both by their GCF (6) to get 2/3.