# QuotientRemainder

QuotientRemainder[m,n]

gives a list of the quotient and remainder from division of m by n.

# Details • QuotientRemainder is also known as the ratio and quantity "left over" from division of m by n.
• Integer mathematical function, suitable for both symbolic and numerical manipulation.
• QuotientRemainder[m,n] returns the ratio of m,n and the quantity "left over".
• # Examples

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## Basic Examples(2)

Compute the quotient and remainder of two numbers:

Plot the sequence of quotients:

Plot the sequence of remainders:

## Scope(7)

QuotientRemainder works over integers:

Rational numbers:

Inexact real numbers:

Exact numbers:

Complex numbers:

Compute for large integers:

QuotientRemainder threads elementwise over lists:

## Applications(8)

### Basic Appications(3)

Plot the quotient of a number of division by 5:

Plot the remainder of a number of division by 5:

Plot the quotient of two integers:

### Number Theory(5)

Use NestWhileList to compute the quotient of positive arguments:

Compare with:

Use Floor to compute the quotient for integers:

Demonstrate how division works:

Count the number of positive integers less than 1000 divisible by 2 or 3, but not divisible by 6:

Direct count:

The Euclidean algorithm:

Compare with:

## Properties & Relations(2)

The first part of QuotientRemainder is the Quotient:

The second part of QuotientRemainder is the Mod:

## Neat Examples(2)

Plot the arguments of the Fourier transform of the QuotientRemainder:

Plot the Ulam spiral of the QuotientRemainder: