The theory of compact linear operators between Banach spaces has a classical core and is familiar to many. Perhaps lesser known is the factorization of compact maps through a closed subspace of c0 [2]. This factorization theorem has a number of important connections and consequences analogous to how the ideals of continuous linear operators factoring compactly through lp-spaces (1 ≤ p < ∞ ) (see [1] and the references therein). In this talk, even though hypercyclic operators are not compact, we consider operator ideals generated by hypercyclic backward weighted shifts and examine their factorization properties.