What's the Answer?

Question

Suppose you're in a hallway lined with 100 closed doors.
You begin by opening every door. Then you close every second door. Then you go to every third door and open it (if it's closed) or close it (if it's open). Let's say you're toggling a door. Continue toggling every nth door on pass number n. After 100 passes, where you toggle only door #100, how many doors are open?

Answer 1

Hint: Which numbers less than 100 have an odd
number of divisors. How many of them are there?

Answer 2

@#%$?