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In computing, the modulo (sometimes called modulus, or mod) operation "9 mod 3" would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and



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Modulo Operation (mod) Algorithm and Examples

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

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

won't 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. When either a or n is negative, the naive definition breaks down and programming languages differ in how these values are defined.

Example

1 mod [ int( )] a n a na n

269.86

100
[269.86] [ int( )]

269 [100 int( )]

269 [100 int(2.6986)]269 [100 2]

69
a n n

Example

2 (log ) mod 1 [100 10 ] mod 100 t Pb t M

Step 1.

2.4311

1 (log ) mod 1 =log(269.86) mod 1

2.4311 mod 1

2.4311 [1 int( )]

2.4311 2

0.4311

t P Step 2 . 0.4311

269.83

100
[100 10 ] mod 100 =[100 2.6983] mod 100

269.83 - [100 int( )]

269.83 200

69
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