A
prime number (or a
prime) is a
natural number greater than 1 that has no positive
divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a
composite number. For example, 5 is prime because 1 and 5 are its only positive integer
factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The
fundamental theorem of arithmetic establishes the central role of primes in
number theory: any
integer greater than 1 can be expressed as a product of primes that is unique
up to ordering. The uniqueness in this theorem
requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 × 3, 1 × 1 × 3, etc. are all valid factorizations of 3.