For questions about factoring elements of rings into primes, or about the specific case of factoring natural numbers into primes.

A natural number is prime if it has no positive divisors besides $1$ and itself. The fundamental theorem of arithmetic states that every natural number $n>1$ can be factored uniquely, up to a reordering of the factors, as a product of distinct prime numbers each raised to some power.

This concept holds in a more general setting though. A ring is called a unique factorization domain (UFD) if every non-unit element can be factored uniquely as a product of prime elements in the ring. The ring of integers is an example of a UFD.