What is the remainder left when $2014!$ is divided by 2017?

The answer is 1008.

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It is easy to see that, with N is a prime number: $(N-1)! \mod(N)=N-1 \Rightarrow 2016! \mod(2017)=2016$ Because: $2015 \times 2016 \mod(2017)=2 \Rightarrow 2014! \mod(2017)=\boxed{1008}$