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)
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(2)
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(3)
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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.