# Integer division¶

The *integer division* or *quotient* of two numbers, written `//`

,
is the result of the division *rounded down* to the nearest integer.
Intuitively, you can think of it as the number of times that one thing
fits into another, disregarding any remainder. For
example, `11 // 2`

is `5`

, because `2`

fits into `11`

five
times (with some left over).

```
Disco> 11 // 2
5
Disco> 6 // 2
3
Disco> 6 // 7
0
Disco> (-7) // 2
-4
```

In fact, `//`

is simply defined in terms of regular division along with the floor operation:

```
x // y = floor (x / y)
```

Although dividing two integers using the usual `/`

operator does not necessarily result in an integer, using integer
division does. In particular, the integer division operator can be given the types

```
~//~ : ℕ × ℕ → ℕ
~//~ : ℤ × ℤ → ℤ
```

Formally, the result of `//`

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

is the unique number \(q\) such that \(n
= qd + r\), where \(0 \leq r < d\).