There are $100$ closed locked in a hallway. A man begins by opening all $100$ lockers. Next, he closes every second locker. Then, on his third pass, he toggles every third locker $($closes it if it is open or opens it if it is closed$).$ This process continues for $100$ passes, such that on each pass $i,$ the man toggles ever $i$ th loeker. After his $100$th pass in the hallway, in which he toggles only locker #$100,$ how many lockers are open? Explain your answer.