  We prove a general theorem showing that iterated skew polynomial extensions
of the type which fit the conditions needed by Cauchon's deleting derivations
theory and by the Goodearl-Letzter stratification theory are unique
factorisation rings in the sense of Chatters and Jordan. This general result
applies to many quantum algebras; in particular, generic quantum matrices and
quantized enveloping algebras of the nilpotent part of a semisimple Lie algebra
are unique factorisation domains in the sense of Chatters. By using
noncommutative dehomogenisation, the result also extends to generic quantum
grassmannians.
