> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/501-number-theory/615-arithmetic/divisor.md).

# Divisor

<https://en.wikipedia.org/wiki/Divisor>

divisor factor multiple divisible by divisibility divisibility rule

A **divisor** or **factor** of an integer $$n$$ is an integer $$m$$ that may be multiplied by some integer $$k$$ to produce $$n$$, that is, $$n = k\cdot m$$. This implies that any $$n$$ has 1 and itself as factors, $$n=n\cdot1$$.

It can also be stated that $$n$$ is a **multiple** of $$m$$; and also of $$k$$.

An integer $$n$$ is **divisible by** another integer $$m$$ if $$m$$ is a divisor of $$n$$, which implies that dividing $$n$$ by $$m$$ leaves no remainder.