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In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient. Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, 10 / 3 leaves a remainder of 1, as 10 is not a multiple of 3.
In an equation =, a is the dividend, b the divisor, and c the quotient. Division by zero is considered impossible at an elementary arithmetic level. Two numbers can be divided on paper using long division. An abbreviated version of long division, short division, can be used for smaller divisors.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Scheme offer two functions, remainder and modulo – Ada and PL/I have mod and rem, while Fortran has mod and modulo; in each case, the former agrees in sign with the dividend, and the latter with the divisor. Common Lisp and Haskell also have mod and rem, but mod uses the sign of the divisor and rem uses the sign of the dividend.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
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The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor. That is, c = a b {\displaystyle c={\tfrac {a}{b}}} is equivalent to c ⋅ b = a . {\displaystyle c\cdot b=a.}