Coprime factorization is a well-known issue in one-dimensional systems theory, having many applications in realization theory, balancing, controller synthesis, etc. Generalization to systems in more than one independent variable is a delicate matter: First of all, several non-equivalent coprimeness notions have to be taken into account. Even worse, the sheer concept of a factorization has to be recast to be appropriate for multidimensional systems theory.