If the number 42573 * is exactly divisible by 72, then the minimum value of * is:

To find the minimum value of , the number 42573 must be divisible by both 8 and 9 (since 72 is a product of 8 and 9) due to the rule of divisibility.

1. For a number to be divisible by 8, the last three digits must be divisible by 8. Here, we have 73*.

   The smallest number that can be formed is 730 which is not divisible by 8. The next smallest number is 731 which is also not divisible by 8. We continue this process until we find a number that is divisible by 8. The smallest such number is 736.

2. Now, for a number to be divisible by 9, the sum of its digits must be divisible by 9. The sum of the digits in 42573 is 21. Adding 6 (from step 1) to this sum gives 27, which is divisible by 9.

Therefore, the minimum value of * that makes 42573* divisible by 72 is 6.