# Definition:Divisor (Algebra)/Integer/Aliquant Part

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## Definition

An **aliquant part** of an integer $n$ is a positive integer which is less than $n$ but is not a divisor of $n$.

## Also known as

Euclid's term for an **aliquant part** is **parts**.

In the words of Euclid:

(*The Elements*: Book $\text{VII}$: Definition $4$)

Referring to **aliquot part** and **aliquant part** as **part** and **parts** respectively can be the source of considerable confusion when it is necessary to refer to the plural forms of either term.

Hence the use of **part** or **parts** for these concepts is heavily deprecated.

For historical reasons, and historical reasons only, the terms **part** and **parts** have been retained in the material quoted directly from Euclid's *The Elements*.

## Also see

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**aliquant part** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**aliquant part** - 2021: Richard Earl and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(6th ed.) ... (previous) ... (next):**aliquant part**