10. A total of 240 students participating in a large group performance stand in a row facing the coach, and they report numbers from left to right as $1,2,3,4$, $5, \cdots$, in sequence. The coach asks all students to remember their reported numbers and perform the following actions: First, all students who reported numbers that are multiples of 3 turn around; then, all students who reported numbers that are multiples of 5 turn around; finally, all students who reported numbers that are multiples of 7 turn around. Questions:
(1) How many students are still facing the coach at this point?
(2) Among the students facing the coach, what is the number reported by the 66th student from left to right?
10. (1) Let $A=\{1,2, \cdots, 240\}, A_{i}$ denote the set of all multiples of $i$ in $A$. Then
$$
\begin{array}{l}
|A|=240 ;\left|A_{3}\right|=\left[\frac{240}{3}\right]=80, \\
\left|A_{5}\right|=\left[\frac{240}{5}\right]=48,\left|A_{7}\right|=\left[\frac{240}{7}\right]=34 ; \\
\left|A_{15}\right|=\left[\frac{240}{15}\right]=16,\left|A_{21}\right|=\left[\frac{240}{21}\right]=11, \\
\left|A_{35}\right|=\left[\frac{240}{35}\right]=6 ;\left|A_{105}\right|=\left[\frac{240}{105}\right]=2 .
\end{array}
$$

Therefore, we have $|A|-\left(\left|A_{3}\right|+\left|A_{5}\right|+\left|A_{7}\right|\right)+2\left(\left|A_{15}\right|+\left|A_{21}\right|+\right.$ $\left.\left|A_{35}\right|\right)-4\left|A_{105}\right|=136$ students facing the coach.