GCD Calculator

Use our free GCD calculator to find the greatest common divisor of two or more numbers with Euclidean algorithm steps and extended GCD (Bezout coefficients).

Math

Mode

Numbers

Formula

The greatest common divisor (GCD) is the largest positive integer that divides all given numbers. Uses the Euclidean algorithm for efficient computation.

GCD(a, b) = GCD(b, a mod b), Euclid's algorithm

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode: basic GCD, step-by-step Euclidean, or extended GCD.
2For basic/steps: enter 2+ numbers. For extended: enter exactly 2 numbers.
3Click Calculate.

Examples

GCD of 48, 18

1.48 ÷ 18 = 2 remainder 12
2.18 ÷ 12 = 1 remainder 6
3.12 ÷ 6 = 2 remainder 0
4.GCD = 6

Result: 6

Extended GCD 48, 18

1.48×(-1) + 18×3 = 6

Result: 6

Coprime 14, 25

1.GCD = 1, numbers are coprime

Result: 1

Frequently Asked Questions

The largest integer that divides all numbers without remainder.

Repeatedly apply GCD(a,b) = GCD(b, a mod b) until remainder is 0.

Finds x, y such that ax + by = gcd(a,b) (Bezout coefficients).

They are mathematically identical.

GCD(0, n) = |n|. All non-zero input required here.

Related Calculators

GCF Calculator LCM Calculator Factors Calculator Divisibility Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-14

GCD Calculator

Formula

How It Works

Examples

GCD of 48, 18

Extended GCD 48, 18

Coprime 14, 25

Frequently Asked Questions

What is GCD?

What is Euclidean algorithm?

What is extended GCD?

GCD vs GCF?

Can GCD be 0?

Related Calculators

GCD Calculator

Formula

How It Works

Examples

GCD of 48, 18

Extended GCD 48, 18

Coprime 14, 25

Frequently Asked Questions

What is GCD?

What is Euclidean algorithm?

What is extended GCD?

GCD vs GCF?

Can GCD be 0?

Related Calculators