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:

A number is a part of a number, the less of the greater, when it measures the greater;

(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.


Also see


Linguistic Note

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


Sources