(Fermat 2024, Part C, Question 24, CEMC - UWaterloo)

The integer $N$ is the smallest positive integer that is a multiple of $2024$, has more than $100$ positive divisors (including $1$ and $N$), and has fewer than $110$ positive divisors (including $1$ and $N$). What is the sum of the digits of $N$?

Answer Submission Note(s)
Your answer should be an integer from 0 to 99, inclusive.
Do NOT code a single digit answer with a leading zero, as you would in the actual contest.