Modulo Operation

Modulo Operation

In computing, the modulo operation, sometimes also called "remainder" or "rest", gives the remainder from a division. It finds the remainder of division of one number by another.

In general, when talking about arithmetic operations, we recognize the following operations:

Additiona + bthe sum of a and b
Subtraction a - bb subtracted from a
Negation- aminus a
Multiplicationa * ba multiplied by b
Divisiona / ba divided by b
Moduloa % bthe remainder of a division between a and b

Given two numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder, on division of a by n.

For example, if you divide 7 by 3, 3 goes in 7 two times. But there is a remainder of 1, and that is the result of the modulo operation.

The expression "9 mod 3" would evaluate to 0.

Although typically performed with a and n both being integers, many computing systems allow other types of numeric operands. There are various ways of defining a remainder, and computers and calculators have various ways of storing and representing numbers, so what exactly constitutes the result of a modulo operation depends on the programming language and/or the underlying hardware.

With floating-point division, such as in 9.0 / 4.0, the result is a floating-point value, in this case 2.25. But with integer division, such as in 9 / 4, the result is only the integer part, in this case 2.

Modulo in calculators

Some calculators have a mod() function button, and many programming languages have a mod() function or similar, expressed for example as mod(a,n).

Some calculators display expressions on the keyboard that say "%", "mod", or "Mod" as a modulo or remainder operator, such as a % n or a mod n.


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