Introduction:
To find the greatest three-digit number that can be exactly divided by 60, 90, and 80, we need to determine the common multiples of these three numbers first. Then, we can find the greatest common multiple that is within the three-digit range (100-999).

Step 1: Find the common multiples:
To find the common multiples of 60, 90, and 80, we can start by finding the multiples of the largest number, which is 90.

Multiples of 90:
90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, ...

Next, we check which multiples of 90 are also multiples of 60 and 80.

Multiples of 90 that are also multiples of 60:
180, 360, 540, 720, 900, 1080, ...

Multiples of 90 that are also multiples of 80:
720, 1080, ...

Step 2: Find the greatest common multiple within the three-digit range:
From the list of common multiples above, we can see that the greatest common multiple within the three-digit range is 900.

Explanation:
The number 900 is divisible by 60, 90, and 80 because it is a multiple of all three numbers. Therefore, it is the greatest three-digit number that can be exactly divided by 60, 90, and 80.

Conclusion:
The greatest three-digit number that can be exactly divided by 60, 90, and 80 is 900.