14. (15 points) Fill in the grid with numbers 1 to 9. Each cell should contain one integer, and different cells should contain different numbers. Additionally, the sum of the numbers in the cells adjacent to (i.e., sharing a common edge with) each cell must be an integer multiple of the number in that cell. It is known that the cells to the left and right are already filled with the numbers 4 and 5, respectively. Question: What is the largest number that can be filled in the cell marked with the letter $x$?

Fill in the grid with numbers 1 to 9. Each cell should contain one integer, and different cells should contain different numbers, and the sum of the numbers in the cells adjacent to each cell must be an integer multiple of the number in that cell. It is known that the cells to the left and right are already filled with the numbers 4 and 5, respectively. What is the largest number that can be filled in the cell marked with the letter $x$?
【Analysis】According to the problem, among the numbers from 1 to 9, excluding 4 and 5, there are only 7 numbers left. The sum of these 7 numbers is 36. The middle number $x$ can only be 3, 6, or 9. Therefore, we can test each one to determine the value of $x$.

【Solution】Solution: According to the analysis, $1+2+3+6+7+8+9=36$. The number $x$ that is filled in must be a factor of the other five numbers, so $x$ can only be 3, 6, or 9. If $x=9$, then it is impossible for the sum of the surrounding numbers of each number to be an integer multiple of the number in that cell;  
When $x=6$, as shown in the figure, it is easy to see that $x=6$ meets the requirements.  
Therefore, the answer is: 6.