Given integers a and b, then we say a divides b if and only if there is some q such that b=qa.

There are many other ways in common use to express this relationship:

  • ab (read “a divides b”).

  • b is divisible by a.

  • a is a factor of b.

  • a is a divisorMathworldPlanetmathPlanetmath of b.

  • b is a multiple of a.

The notion of divisibility can apply to other rings (e.g., polynomials).

Title divisibility
Canonical name Divisibility
Date of creation 2013-03-22 11:59:49
Last modified on 2013-03-22 11:59:49
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 11
Author mathcam (2727)
Entry type Definition
Classification msc 11A51
Synonym divides
Synonym divisor
Synonym factor
Synonym multiple
Related topic LeastCommonMultiple
Related topic ExampleOfGcd
Related topic TauFunction
Related topic ExactlyDivides
Related topic DivisorSumOfAnArithmeticFunction
Related topic StrictDivisibility
Related topic FundamentalTheoremOfArithmetic
Related topic NumberTheory