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 .
See also
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References
Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Divides." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Divides.html