Question 27
Let $m$ be the product of all positive integer divisors of $360{,}000$. Suppose the prime factors of $m$ are $p_{1}, p_{2}, \ldots, p_{k}$, for some positive integer $k$, and $m = p_{1}^{e_{1}} p_{2}^{e_{2}} \cdot \ldots \cdot p_{k}^{e_{k}}$, for some positive integers $e_{1}, e_{2}, \ldots, e_{k}$. Find $e_{1} + e_{2} + \ldots + e_{k}$.