A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number.

So, if n > 0 is an integer and there are integers 1 < a, b < n such that n = a × b, then n is composite. By definition, every integer greater than one is either a prime number or a composite number. The number one is a unit – it is neither prime nor composite. For example, the integer 14 is a composite number because it can be factored as 2 × 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself.

The first 105 composite numbers (sequence A002808 in OEIS) are

Every composite number can be written as the product of two or more (not necessarily distinct) primes; furthermore, this representation is unique up to the order of the factors. This is called the fundamental theorem of arithmetic.

There are several known primality tests that can determine whether a number is prime or composite, without necessarily revealing the factorization of a composite input.