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How many of the factorials from 1! to 100! are divisible by 9?

 Feb 11, 2018
 #1
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100 - 6 + 1=95 Numbers between 6(inclusive) and 100(inclusive) numbers.

 Feb 11, 2018
 #2
avatar+97555 
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How many of the factorials from 1! to 100! are divisible by 9?

 

9! up to 100! all have 9 as one of the factors. so that is 100-9+1=92   (assuming 100! id included)

 

6! = 1*2*3*4*5*6 = 2*4*5*18 = 2*4*5*2*9 

so 6!, and above all have 9 as a factor,  so I will include 6!, 7!, and 8!    92+3=95 so far.

 

5!=1*2*3*4*5  9 is not a factor.

 

So 95 of them have 9 as a factor

 Feb 12, 2018

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