Modular Inverse Calculator
Find an exact multiplicative inverse modulo an integer and inspect the Euclidean divisions and verification residue.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Reduce the signed integer to its nonnegative residue. Apply the extended Euclidean algorithm. Require a greatest common divisor of one. Normalize the inverse and verify its product modulo the modulus.
a×inverse≡1 (mod m), possible exactly when gcd(a,m)=1
Worked example
The inverse of 3 modulo 11 is 4 because 3×4 leaves remainder 1.
Assumptions and input details
Whole-number inputs contain at most sixty digits. The modulus must exceed one. When the values are not coprime, no multiplicative inverse exists; the calculator reports that result explicitly.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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