n! mod 15 = 0  for  



Therefore,  you just need to look at 1!+2!+3!+4! = 1+2+6+24 = 33



33 mod 15 =  

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
 .


Each term  k!,  where k >= 5, is divisible by 15 without a remainder, since it contains factors 3 and 5.


THEREFORE,  the sum  1! + 2! + 3! + . . . + 95! gives the same remainder when is divided by 15, as


    1! + 2! + 3! + 4!,   which is equal to  1 + 2 + 6 + 24 = 33.


The remainder of 33 when divided by 15 is 3.


THEREFORE, the  ANSWER  to the problem's question is  3.




Solved.







 

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