  In this article we investigate the coprimeness properties of one and
two-dimensional discrete equations, in a situation where the equations are
decomposable into several factors of polynomials. After experimenting on a
simple equation, we shall focus on some higher power extensions of the Somos-4
equation and the (1-dimensional) discrete Toda equation. Our previous results
are that all of the equations satisfy the irreducibility and the coprimeness
properties if the r.h.s. is not factorizable. In this paper we shall prove that
the coprimeness property still holds for all of these equations even if the
r.h.s. is factorizable, although the irreducibility property is no longer
satisfied.
