Modular Inverse Calculator

Calculate the multiplicative inverse in modular arithmetic

Number (a)

The number for which to find the modular inverse

Modulus (m)

The modulus must be a positive number

About Modular Inverse

The modular multiplicative inverse of a number a modulo m is a number x such that: (a × x) ≡ 1 (mod m)

For example, the modular inverse of 3 modulo 7 is 5 because:
(3 × 5) = 15 ≡ 1 (mod 7)

Important Notes:

A modular inverse exists if and only if a and m are coprime (their greatest common divisor is 1).
This calculator uses the Extended Euclidean Algorithm to efficiently compute the modular inverse.
The result is always in the range [0, m-1].

Applications:

Cryptography (RSA algorithm)
Solving linear congruences
Number theory problems
Computer science algorithms