Can you fill in 9 different natural numbers in a $3 \times 3$ grid (as shown in the figure) so that the product of the three numbers in each row, each column, and both diagonals equals 2005? If yes, please provide an example. If not, please explain why.
6. Answer: No

Analysis: If it could be filled, then the 9 different natural numbers filled in would be 9 different divisors of 2005. However, 2005 has only 4 different positive divisors: $1, 5, 401$, and 2005, so it cannot be done.