14. There is a rectangular room that is 5.25 meters long and 3.25 meters wide. Now, square tiles are used to cover the floor, and it is required to exactly cover the entire room. What is the maximum side length of the square tiles used?
14. Solution: To pave the entire room with square tiles, the maximum side length of the tiles should be the greatest common divisor (GCD) of the room's length and width. To eliminate decimals, we use centimeters as the unit of length, with the room's length being 525 cm and the width 325 cm. White text
$$\begin{array}{l}
(525,325)=5 \times(105,65) \\
\quad=5 \times 5 \times(21,13)=5 \times 5=25
\end{array}$$

So $(525,325)=25$.
Answer: The maximum side length of the tiles is 25 cm.