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Numbers, Units & Calculators

Extended GCD Calculator

Calculate a result with Extended GCD from the values you enter. Enter the required values, adjust the options, and review the calculated result.

Tool workspace

Your input stays in this browser.

Add the required input to continue.

Needs input

You can run the tool again after any change.

Options

Your result appears here

Calculate a result with Extended GCD from the values you enter. Enter the required values, adjust the options, and review the calculated result.

This tool runs open-source code from CyberChef by GCHQ (Apache License 2.0). See open-source credits.

Extended GCD Calculator finds gcd(a,b) and Bézout coefficients x and y.

It returns coefficients satisfying 30x + 12y = gcd(30,12). The calculation runs in your browser. Processing runs in the browser.

Instructions

  1. Provide values for this tool.
  2. Enter integer values a and b.
  3. Check both value fields.
  4. Verify the Bézout identity in the result.

Example

Input: a = 30; b = 12

Settings: Extended GCD Calculator: Value a: 30; value b: 12.

Result: It returns coefficients satisfying 30x + 12y = gcd(30,12).

Limits

  • Extended GCD Calculator: Inputs must be integers.
  • Extended GCD Calculator: Blank a or b falls back to Input.
  • Extended GCD Calculator: It does not solve non-integer equations.

Questions

What input does Extended GCD Calculator accept?

Extended GCD Calculator accepts text. Computes the Extended Euclidean Algorithm for integers a and b. Finds integers x and y (Bezout coefficients) such that: a*x + b*y = gcd(a, b) This is fundamental to many number theory algorithms including modular inverse, solving linear Diophantine equations, and cryptographic operations. Input handling: If either a or b is left blank, its value is taken from the Input field.

Which settings does Extended GCD Calculator provide?

Extended GCD Calculator provides controls for Value a, Value b.

What does Extended GCD Calculator return?

Extended GCD Calculator returns text. Computes the Extended Euclidean Algorithm for integers a and b. Finds integers x and y (Bezout coefficients) such that: a*x + b*y = gcd(a, b) This is fundamental to many number theory algorithms including modular inverse, solving linear Diophantine equations, and cryptographic operations. Input handling: If either a or b is left blank, its value is taken from the Input field.