How many numbers between $1$ and $6042$ (inclusive) are relatively prime to $3780$? How many numbers between $1$ and $6042$ (inclusive) are relatively prime to $3780$?

Hint: $53$ is a factor.

Here the problem is not the solution of the question, because I would simply remove all the multiples of prime factors of $3780$.
But I wonder what is the trick associated with the hint and using factor $53$.

Maybe they wanted you to rewrite $$6042 = 2\cdot53 \cdot3\cdot19 = (105+1)(56+1) = 2^3\cdot 3\cdot5\cdot 7^2 + 105 + 56 + 1$$
It's easy to compute the numbers from $1$ to $N=2^3\cdot3\cdot5\cdot 7^2$ relatively prime to $m=2\cdot 3\cdot5\cdot 7$ via $\frac{\phi(m)N}{m}=2^2\cdot 2 \cdot 4 \cdot 6\cdot 7$.
You now only have to count the ones from $1$ to $105+56+1 = 162$ which are relatively prime to $m$.
