Definition:Composite Number

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Definition

A composite number $c$ is a positive integer that has strictly more than two positive divisors.

That is, an integer greater than $1$ which is not prime is defined as composite.


In the words of Euclid:

A composite number is that which is measured by some number.

(The Elements: Book $\text{VII}$: Definition $13$)


Sequence of Composite Numbers

Definition:Composite Number/Sequence

Extension to Negative Integers

The definition of a composite number can be extended to the negative integers, as follows:

A negative integer $n$ is composite if and only if $\size n$ is composite.


Special Cases

$0$ is not considered composite.

$1$ is also a special case - it is neither prime nor composite.

All of the other positive integers are either prime or composite.


Plane Number

A plane number is the product of two (natural) numbers.


In the words of Euclid:

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 $\text{VII}$: Definition $16$)


Solid Number

A solid number is the product of three (natural) numbers.


In the words of Euclid:

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 $\text{VII}$: Definition $17$)


Also known as

Some sources refer to a composite number as a factorable or factorizable number.

For many reasons, one being that composite is of fewer syllables and therefore more economical to say, composite is the preferred form on $\mathsf{Pr} \infty \mathsf{fWiki}$.


Examples

Example: $8$

$8$ is a composite number, because:

$8 = 4 \times 2$

and so has $1$, $2$, $4$ and $8$ as divisors.

Thus it has more than $2$ positive divisors, and hence is so classified.


Also see

  • Results about composite numbers can be found here.


Historical Note

The concept of classifying numbers as prime or composite appears to have originated with the Pythagoreans.


Sources

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