The quotient remainder theorem, also often called *the division algorithm*, deals with Euclidean division: the division of one integer by another resulting in a quotient and a remainder. The theorem is a way of restating the result of long division. It states that:

Given any integer and an integer , there exists two unique integers and such that:

where

.

is the dividend, is the divisor, is the quotient, and is the remainder.

The theorem takes this form because in Euclidean division and must all be integers. Ignoring this constraint and rearranging the equation by dividing both sides by yields an equation that may better illustrate the variables and their roles:

The result of division is undefined when the divisor .

« Back to Glossary Index