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

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## Definition

An **aliquot part** of an integer $n$ is a divisor of $n$ which is strictly less than $n$.

## Also known as

Euclid's term for an **aliquot part** is just **part**.

In the words of Euclid:

(*The Elements*: Book $\text{VII}$: Definition $3$)

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*.

Some sources give the term as **aliquot divisor**.

## Also see

## Linguistic Note

The word **aliquot** is a Latin word meaning **a few**, **some**, or **not many**.

## Sources

- 1919: Leonard Eugene Dickson:
*History of the Theory of Numbers: Volume $\text { I }$*... (previous) ... (next): Preface - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**aliquot part** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**aliquot part** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**aliquot part** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**aliquot part** - 2021: Richard Earl and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(6th ed.) ... (previous) ... (next):**aliquot part**