Extended GCD (Bézout coefficients)

Client

Find gcd(a,b) and integers x,y with ax+by=gcd—used in modular inverse and crypto homework.

How to use

Enter two integers separated by | or comma.

About Extended GCD (Bézout coefficients)

Extended Euclidean algorithm—gcd plus x,y where ax+by=gcd—local math. The interactive transform on this page runs in your browser tab—Toolcore does not need your paste for the core operation described above.

How to use this page

Paste or type in the main workspace, run the primary action from the toolbar, then copy or download the result. Use Load example when the page offers it, or URL prefill (?q= / ?qb=) so agents and tickets open the same input.

gcd(240, 46) = 2
Coefficients: x=-9, y=47
Check: 240·-9 + 46·47 = 2

Nearby workflows on Toolcore

  • GCD & LCM calculator — Greatest common divisor and least common multiple for two non-negative integers—BigInt, local only. when units or numeric output should be checked on a related calculator.
  • Modulo calculator — Integer remainder and truncated quotient (a mod b)—BigInt math in your browser. when units or numeric output should be checked on a related calculator.
  • Modular inverse calculator — Compute the modular multiplicative inverse with the extended Euclidean algorithm—in your browser. when units or numeric output should be checked on a related calculator.
  • LCM of multiple numbers — Least common multiple of a list of integers—browser-only. when units or numeric output should be checked on a related calculator.

Common use cases

  • Verify Bézout identity for RSA prep exercises.
  • Check whether two numbers are coprime.

Common mistakes to avoid

  • Non-integers

    Only whole numbers are supported.

FAQ

Negative inputs?

Absolute values are used internally; coefficients account for signs.

More tools

Related utilities you can open in another tab—mostly client-side.