This article is about the binary operation mod(a,n). For the (mod n) notation, see Modular arithmetic. For other uses, see Modulo (disambiguation).
Computational operation
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the modulus of the operation).
Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.[1]
For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0.
Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of n is 0 to n − 1 (a mod 1 is always 0; a mod 0 is undefined, being a division by zero).
When exactly one of a or n is negative, the basic definition breaks down, and programming languages differ in how these values are defined.
^Weisstein, Eric W. "Congruence". Wolfram MathWorld. Retrieved 2020-08-27.
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