Description of Modulo, the remainder of a Euclidean division

Modulo is the remainder of a Euclidean division. As a standalone feature, modulo is included in most programming languages. It is treated there as a function or operator, usually with the abbreviation \(mod\) or \(\%\).

In mathematics, it corresponds to the remainder of a division, as described under Euclidean division.

Example \(17 / 5 = 3\) Rest \(2\)

In the example above is modulo = \(2\)

Dividing numbers with different signs also results in different signs for the results. In the following examples the mathematical division and the modulo function as they are integrated in computers are compared.

\(\small 7\,/\, 3 = 2 \; Rest \, 1\) \(\small -7 \,/\, 3 = -2 \; Rest \; -1\) \(\small 7\, / -3 = -2\ \; Rest \; 1\) \(\small -7\,/ -3 = 2 \; Rest \; -1\) |
\(\small 7\,mod\, 3 = 2 \; Rest \; 1\) \(\small -7 \,mod\, 3 = -2 \; Rest \; -1\) \(\small 7\, / -3 = -2 \; Rest \; 1\) \(\small -7\,mod -3 = 2 \; Rest \; -1\) |