An uncoupled Ore algebra is an abstraction of common properties of linear partial differential, shift and q-shift operators. Using uncoupled Ore algebras, we present an algorithm for finding hyperexponential solutions of a system of linear differential, shift and $q$-shift operators, or any mixture thereof, whose solution space is finite-dimensional. The algorithm is applicable to factoring modules over an uncoupled Ore algebra when the modules are also finite-dimensional vector spaces over the field of rational functions.