The Greatest Common Divisor (GCD) of two or more integers is the largest positive integer that divides each of them without a remainder. For example, GCD(12, 18) = 6 because 6 is the largest number that divides both 12 and 18 evenly.

What algorithm does this tool use?

It uses the Euclidean algorithm: gcd(a, b) = gcd(b, a mod b), repeated until the remainder is 0. The last non-zero remainder is the GCD. This method runs in O(log min(a, b)) steps, making it very fast even for large numbers.

Can I find the GCD of more than two numbers?

Yes. Enter as many integers as you like, separated by commas or spaces. The tool applies the Euclidean algorithm pairwise from left to right: gcd(a, b, c) = gcd(gcd(a, b), c).

What happens if one of the numbers is 0?

By convention, gcd(a, 0) = a. If all inputs are 0 the GCD is undefined, and the tool will show an error.

Does the tool handle negative numbers?

Yes. The GCD is always a positive integer, so the tool works with the absolute values of your inputs. GCD(-12, 18) = GCD(12, 18) = 6.

What is the difference between GCD and LCM?

The GCD is the largest number that divides both values; the LCM (Least Common Multiple) is the smallest number divisible by both. They are related by: LCM(a, b) = |a × b| / GCD(a, b).

GCD Calculator

Name: GCD Calculator
Availability: InStock
Author: Nham Vu

Enter two or more integers and instantly find their Greatest Common Divisor with step-by-step Euclidean algorithm breakdown.

Enter Integers

Numbers (comma or space separated)

Quick examples

Enter at least two integers to calculate their GCD.

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Summary

Enter two or more integers and instantly find their Greatest Common Divisor with step-by-step Euclidean algorithm breakdown.

How it works

Enter at least two integers separated by commas or spaces.
The tool validates each value and flags non-integers.
GCD is computed pairwise using the Euclidean algorithm: gcd(a, b) = gcd(b, a mod b).
For more than two numbers the result accumulates: gcd(a, b, c) = gcd(gcd(a, b), c).
Each division step is displayed so you can follow the full derivation.
The final GCD is shown with a plain-language explanation of what it means.

Use cases

Simplify fractions by dividing numerator and denominator by their GCD.
Find the largest tile size that fits evenly into two room dimensions.
Solve number-theory and discrete-math homework problems step by step.
Check coprimeness — a GCD of 1 means the numbers share no common factors.
Compute LCM: LCM(a, b) = |a × b| / GCD(a, b).
Split a group of items into the largest equal bundles with no remainder.
Verify divisibility rules in cryptography and modular arithmetic.
Reduce gear ratios or musical interval ratios to lowest terms.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu