At Admiral Middle School there are 350 lockers in Hallway B, numbered 1 – 350. All of the lockers are closed. Student #2 decides to run through Hallway B and opens every locker that is a
multiple of 2. Student #3 runs through and changes the state of every locker that is a multiple of 3 (if
it is open, he closes it. If it is closed, he opens it). Then student #4 runs through the hall and changes
the state of every locker that is a multiple of 4. Finally, student #5 changes the state of every locker
that is a multiple of 5. How many lockers are open after student #5 runs through Hallway B?