A confusion about UFDs

Question

So I'm new to this concept and when I was reading the definition. It says that if R is a UFD then every non zero element can be written as the product of irreducible elements. So here's my question which is stupid I know. Are these irreducible elements necessarily distinct??

Answer 1

No, the integers are a unique factorization domain and $4=2 \cdot 2$. You have to include the possibility of a unit, which for the integers can only be $-1$, to get the negatives.