# Definition:Composite Number

## 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.

## 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 $\left|{n}\right|$ 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.

### 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.

## 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.