Modular Inverse Calculator
Find x where a·x ≡ 1 (mod m), with the GCD check.
Enter your values
ⓘ Live results
Results
- Modular inverse
- 38
- Check
- 17 × 38 mod 43 = 1
- gcd(a, m)
- 1
- Coprime?
- Yes — the inverse exists
- a mod m
- 17
Quick answer
The modular inverse of a mod m is the x with a·x ≡ 1 (mod m); it exists only when a and m are coprime.
a·x ≡ 1 (mod m)
How to use the Modular Inverse Calculator
- 1Enter the value you want to invert.
- 2Enter the modulus.
- 3If the GCD is not 1 there is no inverse — pick a different modulus.
Worked example
Using the values the calculator loads with:
Inputs
- Value a17
- Modulus m43
Results
- Modular inverse38
- Check17 × 38 mod 43 = 1
- gcd(a, m)1
- Coprime?Yes — the inverse exists
- a mod m17
Frequently asked questions
Where are modular inverses used?
RSA key generation, hash tables, error-correcting codes and any modular arithmetic where you need to 'divide'.
Why must a and m be coprime?
If they share a factor, every multiple of a stays inside that factor's subgroup and can never reach 1.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.