Short division

In arithmetic, short division is a division algorithm which breaks down a division problem into a series of easy steps. It is an abbreviated form of long division. Short division relies on mental arithmetic, which necessarily limits the size of the divisor. For most people, small integer divisors up to 12 are handled using memorised multiplication tables, though some people can use the procedure for larger divisors.

As in all division problems, a number called the dividend is divided by another, called the divisor. The answer to the problem is called the quotient.

Using short division, one can solve a division problem with a very large dividend by following a series of easy steps.

Short division does not use the slash (/) or obelus (÷) symbols. Instead, it displays the dividend, divisor, and quotient (when it is found) in a tableau. An example is shown below, representing the division of 500 by 4. The quotient is 125.

Alternatively the bar may be placed below the number which means the sum proceeds down the page. This is in distinction to long division where the space under the dividend is required for workings:

The procedure involves several steps. As an example, consider 950 divided by 4:

Using the alternative layout the final workings would be:

A common requirement is to reduce a number to its prime factors. This is used particularly in working with vulgar fractions. The dividend is successively divided by prime numbers, repeating where possible:

So 950 = 2 x 5² x 19

When one is interested only in the remainder of the division, this procedure (a variation of short division) ignores the quotient and tallies only the remainders. It can be used for manual modulo calculation or as a test for even divisibility. The quotient digits are not written down.

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