MathNet 2013 Question 9

Let $p$ and $q$ be positive integers such that $p q = 2^{3} \cdot 5^{5} \cdot 7^{2} \cdot 11$ and $\frac{p}{q} = 2 \cdot 5 \cdot 7^{2} \cdot 11$. Find the number of positive integer divisors of $p$.