15. A rectangular piece of wood is 3 feet 5 inches 7 points long, 1 foot and 5 points wide, and 8 inches 4 points thick. It needs to be cut into equally sized cubic blocks, with the volume of each block being as large as possible. What is the edge length of the block?
15. Solution: The side length of the wooden block is clearly the greatest common divisor of the length, width, and thickness of the wood. We use fractions of an inch as the unit of length, since
$$\begin{aligned}
357 & =3 \times 7 \times 17 \\
105 & =3 \times 5 \times 7 \\
84 & =2^{2} \times 3 \times 7
\end{aligned}$$

so $(357,105,84)=3 \times 7=21$.
Answer: The side length of the wooden block is 2 inches and 1 fraction of an inch.