#Numbers-12

What is the remainder when 1!+2!+3!+4!.....+15! is divided by 6?

Solution-

N = 1! + 2! +3! + 4! +........+ 15!
Factorising 6, we get 1*2*3
Now from 3! onwards, every term has at least a "2" and a "3", hence divisible by 6.
We can write N as 6k + 1! + 2! = 6k + 3
So the remainder when N is divided by 6 is 3 ANS

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