It takes ten men ten hours to build a certain wall. How long does it take five men to build the same wall?

You have 100 doors in a row that are all initially closed. You make 100
passes by the doors starting with the first door every time. the first time through
you visit every door and toggle the door (if the door is closed, you open it, if its
open, you close it). the second time you only visit every 2nd door (door #2, #4,
#6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the
100th door.
Question: what state are the doors in after the last pass? which are open which
are closed?