Maths & numbers
Chinese remainder solver
Solve compatible integer congruences, including non-coprime moduli.
A clear answer. Here’s how.
Combines up to 20 congruences using the extended Euclidean algorithm with exact BigInt arithmetic. Each modulus must be positive, and shared-factor congruences must be compatible. Returns the smallest non-negative solution and the combined least-common-multiple modulus. Input integers have at most 80 digits; the final modulus is bounded to 500 digits.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- One remainder,modulus pair per line
2,3 3,5 2,7
Example result
- Smallest non-negative solution
- 23
- Combined modulus
- 105
All solutions are x + k × combined modulus, for integer k. Compatible non-coprime moduli are supported with exact BigInt arithmetic.