# Division (arithmetic)

In arithmetic, **division** is the operation of finding how many copies of one quantity or number are needed to make up another. This may be viewed as a process of repeated subtraction: the *divisor* is repeatedly subtracted from the *dividend* until this can be done no longer; the number of times the subtraction was performed is the *quotient* and whatever is left over is the *remainder*. If the remainder is zero, then the division is said to be *exact*. In any event, the remainder will be less than the divisor.

For example, 13 (dividend) may be divided 4 (divisor) by repeatedly subtracting 4: 13-4 = 9, 9-4 = 5, 5-4 = 1, at which point the process must terminate, with a quotient of 3 and remainder of 1.

Division may also be viewed as the inverse operation to multiplication, seen as repeated addition. Symbolically, if *c* is the product of *a* and 'b',

- <math>a \times b = c ,\,</math>

then *a* is the answer to the questions "How many times must *b* be added to make *c*" or "How many copies of *b* make up *c*" or "By what must *b* be multiplied to yield *c*". We write

- <math>c / b = a \,</math>

or

- <math>c \div b = a .\,</math>