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Math

GCF Calculator

Find the Greatest Common Factor (GCF / GCD) of two or more numbers using the Euclidean algorithm.

What is GCF Calculator?

The Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), is the largest integer that divides two or more numbers without leaving a remainder. It is essential for simplifying fractions, reducing ratios, and solving number theory problems.

How to use

  1. 1 Enter two or more integers separated by commas or spaces.
  2. 2 The GCF appears instantly along with the full factor list for each number.
  3. 3 The 'Common factors' panel shows all shared factors, not just the greatest one.
  4. 4 You can enter as many numbers as you like — the calculator finds the GCF of the entire set.

Formula

The Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), repeated until the remainder is 0. For multiple numbers: GCF(a, b, c) = GCF(GCF(a, b), c).

Example calculation

To find GCF(48, 36): 48 mod 36 = 12, then 36 mod 12 = 0, so GCF = 12. For GCF(48, 36, 84): GCF(48, 36) = 12, then GCF(12, 84) = 12.

Frequently asked questions

What is the difference between GCF and LCM?

The GCF is the largest number that divides all given numbers. The LCM is the smallest number that all given numbers divide into. They are related by: GCF(a,b) × LCM(a,b) = a × b.

How is the GCF used to simplify fractions?

Divide both the numerator and denominator by their GCF. For example, 24/36 simplifies to 2/3 because GCF(24, 36) = 12.

What is the GCF of two prime numbers?

The GCF of two different prime numbers is always 1, since primes have no common factors other than 1.

What does it mean if the GCF is 1?

If GCF(a, b) = 1, the numbers are called coprime or relatively prime. They share no common factors other than 1.

Can I find the GCF of more than two numbers?

Yes. Apply the Euclidean algorithm pairwise: GCF of three numbers equals GCF(GCF(a, b), c). This calculator handles any number of inputs.