Inverse Modulo Calculator

Your details

Multiplicative: find x so that a*x leaves remainder 1 when divided by m. Additive: find x so that a+x leaves remainder 0.
The integer whose inverse you want to find. Can be negative.
The modulus. Must be a positive integer greater than 1.
Inverse (x)Inverse found
4

The modular inverse in the canonical range 0 to m-1

gcd(a, m)1
Verification(3 * 4) mod 11 = 1 (should be 1)
Inverse exists?Yes - gcd(3, 11) = 1

The multiplicative inverse of 3 mod 11 is 4.

  • Multiplying 3 by 4 and taking mod 11 gives 1: (3 * 4) mod 11 = 1.
  • This is unique in the range 1 to 10 - no other value in that range satisfies the equation.
  • Because 11 and 4 are coprime, the inverse is well-defined.

Next stepModular multiplicative inverses are central to RSA encryption, solving modular linear equations, and computing in finite fields.

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