Modulo operation

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus).

Given two positive numbers, $a$ (the dividend) and $n$ (the divisor), $a$ modulo $n$ (abbreviated as $a mod n$ ) is the remainder of the Euclidean division of $a$ by $n$ . For instance, the expression "5 mod 2" would evaluate to 1 because 5 divided by 2 leaves a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. (Note that doing the division with a calculator will not show the result referred to here by this operation; the quotient will be expressed as a decimal fraction.)

Although typically performed with $a$ and $n$ both being integers, many computing systems allow other types of numeric operands. The range of numbers for an integer modulo of $n$ is 0 to $n - 1$ . ( $n$ mod 1 is always 0; $n mod 0$ is undefined, possibly resulting in a division by zero error in computer programming languages.) See modular arithmetic for an older and related convention applied in number theory.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Modulo_operation

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