Chinese Remainder Theorem Calculator

Solve a system of congruences using the Chinese Remainder Theorem.
Find the unique solution x modulo M for up to three simultaneous congruences.

Remainder r1 (x is congruent to r1 mod m1)

Modulus m1

Remainder r2 (x is congruent to r2 mod m2)

Modulus m2

Remainder r3 (x is congruent to r3 mod m3) — set m3 = 0 to use only two congruences

Modulus m3 (0 = ignore third congruence)

Chinese Remainder Theorem