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 ≤ r < |d|. The number q is called the quotient, … 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, the concept of remainder is still necessary. It can … See more

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

• Davenport, Harold (1999). The higher arithmetic: an introduction to the theory of numbers. Cambridge, UK: Cambridge University Press. p. 25. See more

While there are no difficulties inherent in the definitions, there are implementation issues that arise when negative numbers are involved in … 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 … 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
4. ^ Pascal ISO 7185:1990 6.7.2.2 See more