  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 conctact three manifolds.
