# divisibility

Given integers $a$ and $b$, then we say $a$ divides $b$ if and only if there is some $q\in\mathbb{Z}$ such that $b=qa$.

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

• $a\mid b$ (read “$a$ divides $b$”).

• $b$ is divisible by $a$.

• $a$ is a factor of $b$.

• $a$ is a divisor 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