Solution:

Finding the Greatest 4-Digit Number Divisible by 91
To find the greatest 4-digit number that is exactly divisible by 91, we need to follow these steps:

Step 1: Find the Largest 4-Digit Number
- The largest 4-digit number is 9999.

Step 2: Check Divisibility by 91
- To check divisibility by 91, we need to see if the number is divisible by both 13 and 7, as 13 and 7 are prime factors of 91.
- First, check if 9999 is divisible by 13. The sum of the digits of 9999 is 9 + 9 + 9 + 9 = 36, which is not divisible by 13. Therefore, 9999 is not divisible by 13.
- Next, check if 9999 is divisible by 7. The number 9999 is not divisible by 7 as well.

Step 3: Finding the Greatest Number Divisible by 91
- To find the greatest 4-digit number that is exactly divisible by 91, we need to find the largest number less than 9999 that is divisible by both 13 and 7.
- The largest 4-digit number that is divisible by both 13 and 7 is 9949.
- Therefore, the greatest 4-digit number that is exactly divisible by 91 is 9949.

Conclusion:
Therefore, the greatest 4-digit number that is exactly divisible by 91 is 9949.

The answer is 9919. 91×109=9919