composite number

If a prime is a single indivisible brick, a composite number is something you can build out of smaller bricks. The 12 dots that refuse to stay in one line can be arranged as a neat 3-by-4 rectangle — that arrangement is exactly a factorization, and it is what makes 12 composite.

Formally, a composite number is an integer greater than 1 that has at least one positive divisor other than 1 and itself. Equivalently, it can be written as a product of two integers each larger than 1. The first composites are 4, 6, 8, 9, 10, 12. Every integer above 1 is either prime or composite — there is no third kind.

Be careful about the endpoints. The numbers 0 and 1 are neither prime nor composite: 1 is a unit, and 0 has too many divisors to fit either label. Negative numbers are also usually left out of this classification, which is reserved for integers greater than 1.