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On a compact oriented surface of genus   $g$   with   $n\geq 1$   boundary components,   $\delta _1, \delta _2,\ldots , \delta _n$  , we consider positive factorizations of the boundary multitwist   $t_{\delta _1} t_{\delta _2} \cdots t_{\delta _n}$  , where   $t_{\delta _i}$   is the positive Dehn twist about the boundary   $\delta _i$  . We prove that for   $g\geq 3$  , the boundary multitwist   $t_{\delta _1} t_{\delta _2}$   can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn-Morris, who proved this result for   $g\geq 8$  . This fact has immediate corollaries on the Euler characteristics of the Stein fillings of contact three manifolds.

Arbitrarily Long Factorizations in Mapping Class Groups