section_path: Properties/Division
section_name: Division
paragraph_text: Division
  
  In this section, juxtaposed variables such as ab indicate the product 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 a and b with b ≠ 0 there are natural numbers q and r such that
  
  The number q is called the quotient and r is called the remainder of the division of a by b. The numbers q and r are uniquely determined by a and b. This Euclidean division is key to the several other properties (divisibility), algorithms (such as the Euclidean algorithm), and ideas in number theory.