16. Class A, B, and C have 54 students, 48 students, and 72 students respectively. Now, it is planned to organize physical exercise groups within each class, but the number of students in each group must be the same. What is the maximum number of students in each exercise group? How many groups will there be in Class A, B, and C respectively?
16. Solution: Since students from each class must be organized into exercise groups, and the number of students in each group is the same, the number of students in each group must be a common factor of the number of students in the three classes. Therefore, finding the maximum number of students in a group is equivalent to finding the greatest common divisor (GCD) of the number of students in the three classes. Given
$$\begin{array}{l}
54=2 \times 3 \times 3 \times 3=2 \times 3^{3} \\
48=2 \times 2 \times 2 \times 2 \times 3=2^{4} \times 3 \\
72=2 \times 2 \times 2 \times 3 \times 3=2^{3} \times 3^{2}
\end{array}$$

Thus, $(54,48,72)=2 \times 3=6$. Also,
$$\frac{54}{6}=9, \frac{48}{6}=8, \frac{72}{6}=12$$

Answer: The maximum number of students in an exercise group is 6. At this time, Class A has 9 groups, Class B has 8 groups, and Class C has 12 groups.