Question 2
Kelvin the Frog was bored in math class one day, so he wrote all ordered triples $(a, b, c)$ of positive integers such that $a b c = 2310$ on a sheet of paper. Find the sum of all the integers he wrote down. In other words, compute
$$
\sum_{\substack{a b c = 2310 \\ a, b, c \in \mathbb{N}}} (a + b + c)
$$
where $\mathbb{N}$ denotes the positive integers.
$$
\sum_{\substack{a b c = 2310 \\ a, b, c \in \mathbb{N}}} (a + b + c)
$$
where $\mathbb{N}$ denotes the positive integers.