# Modulo

**Modulo** is a math operation that finds the remainder when one integer is divided by another. In writing, it is frequently abbreviated as **mod**, or represented by the symbol **%**.

For two integers **a** and **b**:

a mod b = r

Where **a** is the dividend, **b** is the divisor (or **modulus**), and **r** is the remainder.

## Examples

**11** mod **4** = **3**, because 11 divides by 4 (twice), with **3** remaining.

**25** mod **5** = **0**, because 25 divides by 5 (five times), with **0** remaining.

**3** mod **2** = **1**, because 3 divides by 2 (once), with **1** remaining.

**5** mod **2** = **1**, because *all odd numbers* yield a remainder of **1** when divided by **2**.

## Modular arithmetic and cryptography

**Modular arithmetic** is the field of mathematics which concerns these types of operations, where values "wrap around" (reset to zero) when they reach a modulus value. Modular arithmetic is extremely important in the field of cryptography, which encodes information using modulo operations with large modulus.

Computer abbreviations, Cryptography, Mod, Programming terms