Divide

To divide is to perform the operation of division, i.e., to see how many times a divisor  goes into another number .  divided by  is written  or . The result need not be an integer, but if it is, some additional terminology is used.  is read " divides " and means that  is a divisor of . In this case,  is said to be divisible by . Clearly,  and . By convention,  for every  except 0 (Hardy and Wright 1979, p. 1). The "divisibility" relation satisfies

			(1)
			(2)
			(3)

where the symbol  means implies.

 is read " does not divide " and means that  is not a divisor of .  means  divides  exactly. If  and  are relatively prime, the notation  or sometimes  is used.

REFERENCES:

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.