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If I expand 25*24*23* ... *12*11*10, how many zeros are there at the end of the number I get?

 May 4, 2022
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10 * 11 * 12 * ... * 25 = (10 * 15 * 20 * 25) * (other numbers)

 

The other numbers don't have any factor of 5. We consider 10 * 15 * 20 * 25.

 

10 * 15 * 20 * 25 = 5^5 * 2^3 * 3

 

Pick two even numbers from (other numbers) to make 5^5 * 2^5 = 10^5.

 

There will be 5 zeros at the end.

 May 4, 2022

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