Modular Arithmetic Calculator

Modular Arithmetic

Definition

a mod m gives the remainder when a is divided by m.

For example, 17 mod 5 = 2 because 17 = 3 × 5 + 2.

Key Properties

(a + b) mod m = ((a mod m) + (b mod m)) mod m

(a × b) mod m = ((a mod m) × (b mod m)) mod m

Applications

Modular arithmetic is used in cryptography (RSA), hash functions, clock arithmetic, and check digit algorithms (ISBN, credit cards).