Question 18
What is the largest integer that is a divisor of
$$
\begin{aligned} &(n+1)(n+3)(n+5) \\ &\quad {}\cdot (n+7)(n+9) \end{aligned}
$$
for all positive even integers $n?$
$$
\begin{aligned} &(n+1)(n+3)(n+5) \\ &\quad {}\cdot (n+7)(n+9) \end{aligned}
$$
for all positive even integers $n?$