Othello Puzzle

For my first puzzle I have chosen a puzzle which involves the board game Othello. In this puzzle I will lay out 64 Othello pieces in rows of 10, all black side up.

What I will then do is turn over all the multiples of 1. Clearly all the numbers are multiples of 1, so all of the pieces will be turned over, like this.

After this I will turn over all the multiples of two, which will look like this.

You can probably see where this is going. I will then tun over all the multiples of 3, then 4, then 5, then 6 all the way up to 64. So, the question is, can you tell me which of the Othello pieces will end up with the white side facing upwards? I will give you a slight hint, this problem can be solved without any othello pieces and just some simple maths. 
The solution will be in the next post!