# Modulo¶

The `mod`

operator is used to give the *remainder* when one number
is divided by another.

For example, `11 mod 2`

is `1`

, because `2`

fits into `11`

five
times, with a remainder of 1; `11 mod 4`

is `3`

, because dividing
`11`

by `4`

leaves a remainder of `3`

.

```
Disco> 11 mod 2
1
Disco> 11 mod 4
3
Disco> 6 mod 2
0
Disco> 6 mod 7
6
Disco> (-7) mod 2
1
```

Formally, the result of `mod`

is defined in terms of the “Division
Algorithm”: given a number \(n\) and a positive divisor \(d\), the
remainder `n mod d`

is the unique number \(r\) such that \(n
= qd + r\), where \(0 \leq r < d\) and \(q\) is the
quotient. (For negative divisors, we
instead require \(d < r \leq 0\).)