We study the number of ways of factoring elements in the complex reflection groups
$G(r,s,n)$ as products of reflections. We prove a result that compares factorization numbers in
$G(r,s,n)$ to those in the symmetric group
$S_n$, and we use this comparison, along with the Ekedahl, Lando, Shapiro, and Vainshtein (ELSV) formula, to deduce a polynomial structure for factorizations in
$G(r,s,n)$.