What is the largest five digit number exactly divisible by 88?

The largest five-digit number exactly divisible by 88 is 99968.

Here's how to find it:

1. Identify the largest five-digit number: The largest five-digit number is 99999.

2. Divide by 88: Divide 99999 by 88.
   99999 / 88 = 1136 with a remainder of 31.

3. Calculate the target number: Subtract the remainder from the largest five-digit number.
   99999 - 31 = 99968

4. Verify divisibility: 99968 should be divisible by 88 without a remainder.
   99968 / 88 = 1136

Therefore, the largest five-digit number exactly divisible by 88 is 99968.