page_title: Short division
section_title: Prime factoring
hierarchical_section_title: Short division / Prime factoring
caption_attribution_description: English: An example of manual factorizing.
context_page_description: 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 — whereby the products are omitted and the partial remainders are notated as superscripts.
  As a result, a short division tableau is always more notationally efficient than its long division counterpart — though sometimes at the expense of relying on mental arithmetic, which could limit the size of the divisor. For most people, small integer divisors up to 12 are handled using memorised multiplication tables, although the procedure could also be adapted to the larger divisors as well.
  As in all division problems, a number called the dividend is divided by another, called the divisor. The answer to the problem would be the quotient, and in the case of Euclidean division, the remainder would be included as well.
  Using short division, one can solve a division problem with a very large dividend by following a series of easy steps.
context_section_description: 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
caption: An example of manual factorizing.
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