# What Is a Composite Number?

A composite number is a number that can be divided exactly by at least one number that is not itself or 1.

This means a composite number is any number (other that 1) that is not a prime number.

For example;
• 4 is a composite number. It can be divided exactly by 1, 2 and 4.

4 is a composite number because it can be divided by 2 (which is not 1 or 4 itself).

• 5 is not a composite number. It can only be divided exactly by 1 and 5.

5 is a prime number because it can only be divided by 1 and 5 itself.

#### Dictionary Definition

The Oxford English Dictionary defines a composite number as "a number which is the product of two or more factors, greater than unity."

# The Composite Numbers

The composite numbers are:

In a number square, the composite numbers are shaded below:

Note: This is the exact inverse of the prime numbers in a square. If this number square is overlaid with that of the prime numbers, all numbers (apart from 1) would shaded.

# Composite Numbers, Prime Numbers and the Fundamental Theorem of Arithmetic

The fundamental theorem of arithmetic states that:
Any positive integer greater than 1 is either a prime number, or a unique product of prime numbers.
This means that all composite numbers can be found by multiplying prime numbers together. Any composite number is a product of prime factors.

#### An Example Question

What is 4 as a product of prime numbers?

#### An Example Question

What is 6 as a product of prime numbers?

#### An Example Question

What is 8 as a product of prime numbers?

This process is prime factorisation, as every number can be written as a product of prime factors.

What's more, the product of prime factors are unique to each composite number. 8, for example, can only be found by 2 × 2 × 2. No other group of prime numbers can be multiplied together to find 8.

##### Interactive Test
show

Here's a second test on composite numbers.
Here's a third test on composite numbers.
Here's a dynamic test on composite numbers.

# Composite Numbers Are Natural Numbers Greater Than 1

Composite numbers are natural numbers (the counting numbers: 1, 2, 3...) greater than 1.

# Factors

Numbers that divide exactly into another number are called factors.

For example, the factors of 4 are 1, 2 and 4 because they all divide exactly into 4.

Composite numbers must have more than 2 factors: 1, the composite number itself, and at least one other factor.

This is in distinction to prime numbers which only have two factors: 1 and the prime number itself.