A composite number is a counting number with more than two different factors (or divisors).
Consider the table below. It shows the set of all factors of each number.
| Numbers | Set of Factors | Number of different factors |
|---|---|---|
| 1 | {1} | 1 |
| 2 | {1, 2} | 2 |
| 3 | {1, 3} | 2 |
| 4 | {1, 2, 4} | 3 |
| 6 | {1, 2, 3, 6} | 4 |
| 7 | {1, 7} | 2 |
| 9 | {1, 3, 9} | 3 |
| 10 | {1, 2, 5, 10} | 4 |
| 12 | {1, 2, 3, 4, 6, 12} | 6 |
Some numbers except 1 has at least two factors. Numbers like 2 and 3 are prime numbers.
Numbers with more than two factors like 6 and 12 are composite numbers.
The number 1 = 1 x 1 and 1 is the only factor of 1 therefore it is neither composite nor prime.
From the table above we can say that counting numbers can be placed in one of three sets:
- The set of prime numbers
- The set of composite numbers
- The set with just number 1
