To solve this problem, let's break it down into several clear steps.
### Step 1: Identify the digits
The digits we have are 6, 2, 7, 4, and 3. Each must be used exactly once to form 5-digit numbers.
### Step 2: Form the greatest 5-digit number
To form the greatest possible 5-digit number, arrange the digits in descending order. Sorting the digits in descending order from highest to lowest gives:
- 7
- 6
- 4
- 3
- 2
Putting these digits together forms the number 76432.
### Step 3: Form the least 5-digit number
To form the least possible 5-digit number, arrange the digits in ascending order. Sorting the digits in ascending order from lowest to highest gives:
- 2
- 3
- 4
- 6
- 7
Putting these digits together forms the number 23467.
### Step 4: Calculate the difference
The final step is to find the difference between the greatest 5-digit number and the least 5-digit number:
[tex]\[ 76432 - 23467 = 52965 \][/tex]
### Conclusion
- The greatest 5-digit number is 76432.
- The least 5-digit number is 23467.
- The difference between the greatest and the least 5-digit numbers is 52965.
Thus, when you use the digits 6, 2, 7, 4, and 3 each exactly once, the difference between the greatest and least 5-digit number you can form is 52965.
