Innumber theory, thefundamental theorem of arithmetic, also called theunique factorization theoremor theunique-prime-factorization theorem, states that everyintegergreater than 1[note 1]either is prime itself or is the product ofprime numbers, and that this product is unique, up to the order of the factors.[3][4][5]For example,1200 = 24 31 52= 3 2 2 2 2 5 5 = 5 2 3 2 5 2 2 = etc.The theorem is stating two things: first, that 1200canbe represented as a product of primes, and second, no matter how this is done, there will always be four 2s, one 3, two 5s, and no other primes in the product.The requirement that the factors be prime is necessary: factorizations containingcomposite numbersmay not be unique (e.g. 12 = 2 6 = 3 4).This theorem is one of the mainreasons why 1 is not considered a prime number: if 1 were prime, the factorization would not be unique, as, for example,2 = 21 = 211 = ...