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Find the number of perfect squares that divide 10!.

 Nov 30, 2021
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There are 30 of them as follows:

 

1 , 4 , 9 , 16 , 25 , 36 , 64 , 81 , 100 , 144 , 225 , 256 , 324 , 400 , 576 , 900 , 1296 , 1600 , 2025 , 2304 , 3600 , 5184 , 6400 , 8100 , 14400 , 20736 , 32400 , 57600 , 129600 , 518400 , Total == 30 perfect squares.

 Nov 30, 2021

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