the fundamental theorem of arithmetic (also called the unique factorization theorem) is a theorem of number theory. the theorem says that "every" positive integer greater than 1 can be written as a product of prime numbers (or the integer is itself a prime number). the theorem also says that there is only one way to write the number. if two people found two different ways to write the number, the only thing that can be different is the order in which the primes are written. for example, we can write: