Launois, Lenagan and Rigal proved that many generic quantized coordinate rings and quantum algebras are noncommutative UFDs in the sense introduced by Chatters and Jordan. Other ncUFDs and ``near UFDs" (in which all but finitely many height 1 prime ideals are principal) have appeared in recent joint work with K. Brown. We shall describe these results and relations with the problem of determining the Zariski topology on prime spectra of quantum algebras.