The $1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 ! \quad$ is divisible by

As we know the last two digits of 10 ! and above factorials will be zero-zero. $\therefore 1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 !$ $=1+24+5040+10 !+12 !+13 !$ $+15 !+16 !+17 !$ $=5065+10 !+12 !+13 !+15 !+16 !+17 !$ In this series, the digit in the ten place is 6 which is divisible by $3 !$.