How many of the palms are up and how many are down


Imagine there are 500 people lined up in a row, each person is holding out one palm and it is face down. Then, every single one of the 500 palms has its status changed - that is, all are now face up. Then, every other palm has its status changed (so palms 2, 4, 6 ... are face down again) Then, every third palm has its status changed. Then every fourth palm has its status changed. Then every fifth etc..... All the way to every 500th person having his palm status changed. In the end, how many of the 500 palms are up, and how many are down?

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Mathematics: How many of the palms are up and how many are down
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