Integer division is division in which the fractional part is discarded. For a nonnegative integer 
and a positive integer 
, it returns a quotient 
and remainder 
. The remainder satisfies 
, and the two values are characterized by
 |  |  |
(1)
|
 |  |  |
(2)
|
The quotient is sometimes denoted 
. For example, 
, whereas 
.
For large integers, division can be reduced to multiplication using a whole shifted inverse. Given an integer base 
and 
such that 
, Watt (2023) showed that for some 
,
 |
(3)
|
Thus multiplication by 
, followed by a base-
shift, gives either the quotient or one less than the quotient.
The remainder is then 
.
Integer division is implemented in the Wolfram Language as Quotient[a, b].
