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:
|Addition||a + b||the sum of a and b|
|Subtraction||a - b||b subtracted from a|
|Negation||- a||minus a|
|Multiplication||a * b||a multiplied by b|
|Division||a / b||a divided by b|
|Modulo||a % b||the 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.