The author has introduced the concept of (E,M)-factorization structure on a category C with respect to Pro C and showed that there is a bijection between the class of all E-proreflective subcategories of C and the class of all such (E,M)-factorization structures. In this paper the author studies a characterization of those classes M of rudimentary sources for which there exists a class \(E\subseteq Mor^ r \Pr o C\) such that the pair (E,M) is a factorization structure on C with respect to Pro C.