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How many of the factorials from 1! to 100! are divisible by \(60\)?

 Feb 10, 2022
 #1
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Note  that  1 * 2 * 3 * 4 * 5  =  5!  =   120 = (60 * 2)

 

Then  6!  =  5!  * 6  =   (60 * 2) * 6 =  60 (12)

 

And  every factorial from 7 to 100  will contain  5!  =   60 * 2

 

So from   1!  to  100!  we  will have

 

100 - 5  + 1   =     96 factorials that are divisible by 60

 Feb 10, 2022

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