Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that a = qd + r and 0 … See more

When a and d are floating-point numbers, with d non-zero, a can be divided by d without remainder, with the quotient being another floating-point number. If the quotient is constrained to being an integer, however, th… See more

While there are no difficulties inherent in the definitions, there are implementation issues that arise when negative numbers are involved in calculating remainders. Different programming languages have adopted different co… See more

Euclidean division of polynomials is very similar to Euclidean division of integers and leads to polynomial remainders. Its existence is based on the following theorem: Given two univariate polynomials a(x) and b(… See more

• Chinese remainder theorem
• Divisibility rule
• Egyptian multiplication and division
• Euclidean algorithm… See more

1. ^ Smith 1958, p. 97
2. ^ Ore 1988, p. 30. But if the remainder is 0, it is not positive, even though it is called a "positive remainder".
3. ^ Ore 1988, p. 32 … See more