Modular Inverse Calculator

Understand the modular inverse calculator result

Modular Inverse Calculator is designed for solving congruences, checking hand calculations, and understanding modular division. It asks for integer a, modulus m and reports inverse and check remainder. The extended Euclidean algorithm finds a Bezout coefficient and normalizes it into the modulus range. A valid inverse multiplied by a leaves remainder one after division by the modulus. By exposing inverse and check remainder, Modular Inverse Calculator makes this specific arithmetic inspectable instead of presenting an unexplained number.

With the page defaults of Integer a 3, Modulus m 11, the verified output is Inverse 4, Check remainder 1. Reducing a modulo m first is fine, but dividing ordinary integers is not modular inversion. In Modular Inverse Calculator, each labeled default remains visible while you edit, so you can change one assumption at a time and trace how inverse responds.

Method, limits, and private processing

An inverse exists only when a and the modulus are coprime. Modular Inverse Calculator evaluates the entered values entirely in your browser, without sending the inputs to a server. When using its inverse and check remainder, retain the stated method and input units because this result is bounded by the assumptions of the extended Euclidean algorithm finds a Bezout coefficient and normalizes it into the modulus range.