Definition:Multiple

Definition

Let $\left({D, +, \circ}\right)$ be an integral domain and $x, y \in D$.

If $x \backslash y$, then $y$ is a multiple of $x$.

See divisor.

Euclid's Definition

As Euclid defined it:

The greater is a multiple of the less when it is measured by the less.

(The Elements: Book V: Definition $2$)

... and again:

The greater number is a multiple of the less when it is measured by the less.

(The Elements: Book VII: Definition $5$)

A number is said to multiply a number when that which is multiplied is added to itself as many times as there are units in the other, and thus some number is produced.

(The Elements: Book VII: Definition $15$)

And, when two numbers having multiplied one another make some number, the number so produced is called plane, and its sides are the numbers which have multiplied one another.

(The Elements: Book VII: Definition $16$)

And, when three numbers having multiplied one another make some number, the number so produced is solid, and its sides are the numbers which have multiplied one another.

(The Elements: Book VII: Definition $17$)