Question 12
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 $n?$