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.