I know that every UFD (unique factorization domain) is a GCD domain i.e. g.c.d. of any two elements, not both zero, exists in the domain.
I am looking for an example of a GCD domain which is not a UFD.
I have not been able to find mainly for the difficulty that in a GCD domain every irreducible must be a prime and all the examples of non-UFD's I know, in them some irreducible is not prime.
So please help. Thanks in advance.