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 $53$.

$3780=2^2\cdot3^3\cdot5\cdot7$
Any number that is not co-prime with $3780$ must be divisible by at lease one of $2,3,5,7$
Let us denote $t(n)=$ number of numbers$\le 6042$ divisible by $n$
$t(2)=\left\lfloor\frac{6042}2\right\rfloor=3021$
$t(3)=\left\lfloor\frac{6042}3\right\rfloor=2014$
$t(5)=\left\lfloor\frac{6042}5\right\rfloor=1208$
$t(7)=\left\lfloor\frac{6042}7\right\rfloor=863$
$t(6)=\left\lfloor\frac{6042}6\right\rfloor=1007$
Similarly, $t(30)=\left\lfloor\frac{6042}{30}\right\rfloor=201$
and $t(2\cdot 3\cdot 5\cdot 7)=\left\lfloor\frac{6042}{210}\right\rfloor=28$
The number of number not co-prime with $3780$
=$N=\sum t(i)-\sum t(i\cdot j)+\sum t(i\cdot j \cdot  k)-t(i\cdot j\cdot  k \cdot l)$ where $i,j,k,l \in (2,3,5,7)$ and no two are equal.
The number of number coprime with $3780$ is $6042-N$
Reference: Venn Diagram for 4 Sets
