what is modulo? Explain
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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 example, 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. (a mod 1 is always 0; a mod 0 is undefined, possibly resulting in a division by zero error in programming languages.) See modular arithmetic for an older and related convention applied in number theory.
When either a or n is negative, the naive definition breaks down and programming languages differ in how these values are defined.
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 example, 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. (a mod 1 is always 0; a mod 0 is undefined, possibly resulting in a division by zero error in programming languages.) See modular arithmetic for an older and related convention applied in number theory.
When either a or n is negative, the naive definition breaks down and programming languages differ in how these values are defined.
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