Editing Natural number (section)

===Division===
In this section, juxtaposed variables such as {{math|''ab''}} indicate the product {{math|''a'' × ''b''}}, and the standard [[order of operations]] is assumed.

While it is in general not possible to divide one natural number by another and get a natural number as result, the procedure of ''division with remainder'' or [[Euclidean division]] is available as a substitute: for any two natural numbers {{math|''a''}} and {{math|''b''}} with {{math|''b'' ≠ 0}} there are natural numbers {{math|''q''}} and {{math|''r''}} such that
:<math>a = bq + r \text{ and } r < b. </math>

The number {{math|''q''}} is called the ''[[quotient]]'' and {{math|''r''}} is called the ''[[remainder]]'' of the division of {{math|''a''}} by&nbsp;{{math|''b''}}. The numbers {{math|''q''}} and {{math|''r''}} are uniquely determined by {{math|''a''}} and&nbsp;{{math|''b''}}. This Euclidean division is key to the several other properties ([[divisibility]]), algorithms (such as the [[Euclidean algorithm]]), and ideas in number theory.