div, _div

Integer part of a quotient

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m div n
_div(x, m)


x div m represents the integer q satisfying x = qm + r with 0 ≤ r < |m|.

For positive x and m, q = x div m is the integer part of the quotient x/m, i.e., q = trunc(x/m).

x div m is equivalent to the function call _div(x, m).

An integer is returned if both x and m evaluate to integers. A symbolic expression of type "_div" is returned if either x or m does not evaluate to a number. An error is raised if x or m evaluates to a number that is not an integer.

div does not operate on polynomials. Use divide.


Example 1

With the default setting for mod, the identity (x div m) * m + (x mod m) = x holds for integer numbers x and m:

43 div 13 = trunc(43/13), 43 mod 13 = frac(43/13) * 13

(43 div 13) * 13 + (43 mod 13) = 43

Example 2

Symbolic expressions of type "_div" are returned, if either x or m does not evaluate to a number:

43 div m, x div 13, x div m

type(x div m)

If x or m are numbers, they must be integer numbers:

1/2 div 2
Error: Invalid argument. [div]
x div 2.0
Error: Invalid argument. [div]


x, m

Integers or symbolic arithmetical expressions; m must not be zero.

Return Values

Integer or an arithmetical expression of type "_div".

Overloaded By

m, x

See Also

MuPAD Functions