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Modular Inverse Calculator
Find the number x that makes a × x leave a remainder of 1 when divided by m. See whether an inverse exists, the greatest common divisor, and the extended Euclidean steps.
How do I find a modular inverse?
Enter an integer a and a modulus m of at least 2. An inverse exists exactly when gcd(a, m) = 1. The result is normalized from 0 to m − 1 and verified by multiplication modulo m.
Frequently asked questions
How do I find a modular inverse?
Enter an integer a and a modulus m of at least 2. An inverse exists exactly when gcd(a, m) = 1. The result is normalized from 0 to m − 1 and verified by multiplication modulo m.
Are my numbers sent to a server?
No. The arithmetic runs in your browser and the values are not uploaded or saved by this tool.
What is the inverse of 3 modulo 7?
It is 5 because 3 × 5 = 15, and 15 leaves remainder 1 when divided by 7.
When does a modular inverse exist?
An integer a has an inverse modulo m exactly when a and m are coprime, meaning their greatest common divisor is 1.
What if the input is negative?
The calculator first reduces a to its standard residue from 0 to m − 1. This does not change which inverse exists.