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GCF Calculator (Greatest Common Factor)

Compute the greatest common factor (GCF/HCF/GCD) of any group of numbers with step-by-step methods.

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How to Use the GCF Calculator

1Enter two or more comma-separated whole numbers (e.g. 24, 36, 60).
2Choose your preferred solution breakdown: Euclidean Algorithm or Prime Factorization.
3Click Calculate or see the result update automatically.
4View the common divisors and final greatest factor.

Formula & How It Works

Euclidean Algorithm

a = b × q + r, then GCD(a, b) = GCD(b, r)

The Euclidean algorithm calculates the GCD of two integers a and b by repeatedly taking the remainder: GCD(a, b) = GCD(b, a mod b) until the remainder reaches zero.

Worked Examples

GCF of 48 and 180

Input: 48, 180

Explanation: 180 mod 48 = 36. 48 mod 36 = 12. 36 mod 12 = 0. Therefore, the GCF is 12.

Result: GCF = 12

GCF of Three Numbers (24, 36, 60)

Input: 24, 36, 60

Explanation: GCF(24, 36) = 12. Then GCF(12, 60) = 12.

Result: GCF = 12

Frequently Asked Questions

What is the difference between GCF and LCM?▼

The GCF is the largest number that divides evenly into all given numbers, whereas the LCM is the smallest positive number that is a multiple of all of them.

Can GCF be calculated for negative numbers?▼

Yes, factors of negative integers are considered using their absolute values, so GCF is always a positive integer.

What if the numbers have no common factor besides 1?▼

Numbers whose GCF is 1 are called coprime or relatively prime numbers (e.g., 8 and 9).

How many numbers can I enter?▼

You can enter as many comma-separated numbers as you need.

Last reviewed & updated: 2026-03-25

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