Inspired by Euler

The prime factorization of $2018$ is

$2018$ = $2 \times 1009$

So the number of numbers which are not coprime with $2018$ will be All even numbers upto $2017$ and multiples of $1009$

The no. Of even numbers is $\dfrac{2016}{2}$ $=$ $1008$

The only multiple of $1009$ upto $2017$ is $1009$ itself.

So the no. Of numbers which are coprime will be $=$ total no. Of numbers $-$ numbers which are not coprime

i.e. $2017$ $-$ $1009$ . $=$ $\boxed{1008}$