Divides

If, for  and  integers, the ratio  is itself an integer, then  is said to divide . This relationship is written , read " divides ." In this case,  is also said to be divisible by  and  is called a divisor of .

Clearly,  and . By convention,  for every  except 0 (Hardy and Wright 1979, p. 1).

The function  can be implemented in the Wolfram Language as

  Divides[a_, b_] := Mod[b, a] == 0

The function Divisible[n, d] returns True if an integer  is divisible by an integer .

REFERENCES:

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