Math & Statistics
Chinese Remainder Theorem Calculator
Solve a pair of simultaneous congruences using the Chinese Remainder Theorem.
Your inputs
Change any value to update the result instantly.
Smallest positive solution x
8
Combined modulus
15
Formula and working
x ≡ r₁ (mod m₁), x ≡ r₂ (mod m₂)
- 1
Collect the inputs
Remainder r1 = 2; Modulus m1 = 3; Remainder r2 = 3; Modulus m2 = 5
- 2
Apply the formula
x ≡ r₁ (mod m₁), x ≡ r₂ (mod m₂)
- 3
Result
Smallest positive solution x = 8
Frequently asked questions
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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