Fundamental theorem of arithmetic

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:

6936 = 2³ · 3 · 17²   or   1200 = 2⁴ · 3 · 5²

and if somebody else finds another way to write 6936 or 1200 as product of prime numbers, we can put those prime numbers in the right order and find out that it is the same as what we have here. Finding the prime numbers is called factorization.

This theorem can be used in cryptography.