SOLUTION: Find the remainder when 1! + 2! + 3! ... + 100! is divided by 24

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Question 884958: Find the remainder when 1! + 2! + 3! ... + 100! is divided by 24
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Find the remainder when 1! + 2! + 3! ... + 100! is divided by 24

%281%21%2B2%21%2B3%21%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2B100%21%29%2F24 %22%22=%22%22%281%21%2B2%21%2B3%21%29%2F24%22%22%2B%22%22%284%21%2B5%21%2B6%21%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2B100%21%29%2F24
%281%21%2B2%21%2B3%21%29%2F24 %22%22=%22%22 %281%2B2%2B6%29%2F24 %22%22=%22%22 9%2F24
4! = 4*3*2*1 = 24 is divisible by 24 and all the higher factorials
are also divisible by 24. So %284%21%2B5%21%2B6%21%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2B100%21%29%2F24 is an integer.
So we get an integer plus 9%2F24, so the remainder must be 9.
Edwin