Euclidean division

In arithmetic, the Euclidean division is the process of division of two integers, which produces a quotient and a remainder. There is a theorem stating that the quotient and remainder exist, are unique, and have certain properties. Integer division algorithms compute the quotient and remainder given two integers, the most well-known such algorithm being long division. Euclidean division, and algorithms to compute it, are fundamental for many questions concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, and modular arithmetic, for which only remainders are considered. The operation consisting in computing only the remainder is called the modulo operation.