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Divide

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

b|a and c|b=>c|a
(1)
b|a=>bc|ac
(2)
c|a and c|b=>c|(ma+nb),
(3)

where the symbol => means implies.

d^'n is read "d^' does not divide n" and means that d^' is not a divisor of n. a^k∥b means a^k divides b exactly. If n and d are relatively prime, the notation (n,d)=1 or sometimes n_|_d is used.

See also

Congruence, Divides, Divisible, Divisibility Tests, Division, Divisor, Greatest Dividing Exponent, k-ary Divisor, Relatively Prime

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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

Divide

Cite this as:

Weisstein, Eric W. "Divide." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Divide.html

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