At the end of Lakendra's experiment, are lockers 5, 12, 100,and 856 open or closed?

Question

there are 1000 lockers at Lakendra's school. she opened every second one. then she started over and opened every third one. then she opened every fourth, fifth....1000th locker. if the locker was closed, she opened it, and if it was open she would close it.

Answer 1

This question is easily answered by finding the factors of each number.

For instance, for locker number 5, the factors are:

1 and 5.

Lakendra never opened every single locker--she started with every 2nd locker.

Therefore, the 5th locker was opened when she started on every 5th locker, and it wasn't touched again.

For locker 12: The factors are:

2,3,4,6, and 12.

So, it was open on 2, closed on 3...so on...opened on every 12th locker.

100:

Factors are: 1, 2, 4, 5, 10, 20, 25, 50, 100.

Remember, we aren't counting #1, so:

Open, Closed, Open, Closed etc...on every 100 it will be closed.

For 856:

1,2,4,8,107,214,428,856

It will be Open.

To summarize:

5th: OPEN
12th: OPEN
100th: CLOSED
856th: OPEN

Answer 2

yea