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Composite Numbers (Mathematics Glossary)

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

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.