Calculate modulo (remainder) of any division with quotient and step-by-step solution.
The modulo operation (mod) returns the remainder after dividing one number by another. For example, 17 mod 5 = 2 because 17 ÷ 5 = 3 remainder 2. Written as 17 % 5 = 2 in programming. Our modulo calculator instantly computes the remainder for any two numbers, supporting both positive and negative values.
The modulo operator (%) is one of the most used operators in programming. Common uses: Even/Odd check: if (n % 2 == 0) → even. Cycling through array indices: index = count % array.length. Clock arithmetic: hour = (currentHour + hoursAdded) % 24. Generating patterns: alternating colors, striped rows in tables. Hash functions: hash % tableSize distributes data evenly.
In mathematics, modular arithmetic is a system where numbers "wrap around" after reaching a certain value (the modulus). Clock time is the classic example: 11 + 3 = 14, but 14 mod 12 = 2 (2 PM). Modular arithmetic is fundamental in number theory, cryptography, and solving problems like: "What day of the week will it be in 100 days?"
Modular arithmetic is the mathematical backbone of modern cryptography. RSA encryption uses modular exponentiation. The Diffie-Hellman key exchange is based on discrete logarithms modulo a prime. The reason these systems are secure is that while computing a^b mod n is fast, reversing the operation (finding b given a, a^b mod n, and n) is computationally infeasible for large primes.
Modulo behavior with negative numbers varies by programming language. In Python: -7 % 3 = 2 (result always non-negative, matches mathematical definition). In JavaScript/Java/C++: -7 % 3 = -1 (result has same sign as dividend). When working across languages, be explicit about expected behavior with negative inputs to avoid subtle bugs in your code.
Modulo (mod) is the remainder after dividing one number by another. For example, 17 mod 5 = 2 because 17 ÷ 5 = 3 with remainder 2.
Modulo is widely used in programming for checking even/odd numbers, cycling through arrays, clock arithmetic, and cryptography.
0 mod n = 0 for any non-zero n, because 0 divided by any number gives 0 with no remainder.
Modulo with negative numbers varies by programming language. In mathematics, the result is always non-negative. In Python, -7 mod 3 = 2, not -1.
