The mod
operator is used to give the remainder when one number is divided by <division>
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 ≤ r < d and q is the quotient <integerdiv>
. (For negative divisors, we instead require d < r ≤ 0.)