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Modular Division Calculator — result sheet
Solve a modular division by finding the multiplicative inverse when it exists.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: x≡a×b⁻¹ (mod m), where b×b⁻¹≡1 (mod m) and gcd(b,m)=1.
Modular division is multiplication by an inverse; the calculator rejects a divisor that has no inverse under the selected modulus.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Dividend a — minimum -1000000000000; maximum 1000000000000
- Divisor b — minimum -1000000000000; maximum 1000000000000
- Positive modulus — minimum 2; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Dividend a | 17 |
| Divisor b | 5 |
| Positive modulus | 12 |
17÷5 mod 12 =1 because 5⁻¹=5 mod 12.
Assumptions and limits
- Inputs are whole numbers, modulus is positive, and divisor is coprime to the modulus.
- The returned solution is the least nonnegative residue.
- A set of all congruent integer solutions is not listed.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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