A composite number is a positive integer with three or more divisors. Every integer (excluding one and zero) is either a prime number or a composite number. The integer 14 is a composite number because it has divisors 1, 2, 7, and 14 (four divisors). Note that a square number will always have an odd number of divisors (9 has divisors 1, 3, 9) while a non-square number always has an even number of divisors.

Because the number 1 and the composite number itself are not prime numbers, a composite number can also be defined as "a non-prime number with one or more prime factors".

Properties

• All even numbers greater than 2 are composite numbers.
• All composite numbers are non-primes.
• The smallest composite number is 4.
• <math>(n-1)! + 1\,\,\, \not\equiv \,\, 0 \pmod{n}<math> For all composite number <math>n\,\!<math> greater than 4 (Wilson's theorem).
• <math>(n-1)! \,\,\, \equiv \,\, 0 \pmod{n}<math> For all composite number <math>n\,\!<math> greater than 4 (composite theorem).

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