Find the difference between the greatest and the smallest four-digit numbers formed by using all the digits 8, 6, 7 and 4.

Options

A. 4000
B. 4080
C. -4080
D. 4086

Explanation

To find the difference between the greatest and the smallest four-digit numbers formed using the digits 8, 6, 7, and 4, we can follow these steps:

### Step 1: Identify the digits
The digits we have are 8, 6, 7, and 4.

### Step 2: Form the greatest four-digit number
To form the greatest four-digit number, we need to arrange the digits in descending order (from largest to smallest):
- The largest digit is 8.
- The next largest is 7.
- Then we have 6.
- Finally, the smallest digit is 4.

So, the greatest four-digit number is **8764**.

### Step 3: Form the smallest four-digit number
To form the smallest four-digit number, we arrange the digits in ascending order (from smallest to largest):
- The smallest digit is 4.
- The next smallest is 6.
- Then we have 7.
- Finally, the largest digit is 8.

So, the smallest four-digit number is **4678**.

### Step 4: Calculate the difference
Now, we need to find the difference between the greatest and smallest four-digit numbers:
- Greatest number: 8764
- Smallest number: 4678

We calculate the difference:
\[ 8764 - 4678 \]

### Step 5: Perform the subtraction
Let's subtract step by step:
1. Start from the rightmost digit:
- 4 - 8: We cannot subtract, so we borrow 1 from the next digit (6 becomes 5, and 4 becomes 14).
- 14 - 8 = 6.

2. Next digit:
- 5 - 7: Again, we cannot subtract, so we borrow 1 from the next digit (7 becomes 6, and 5 becomes 15).
- 15 - 7 = 8.

3. Next digit:
- 6 - 6 = 0.

4. Last digit:
- 8 - 4 = 4.

Putting it all together, we have:
\[ 8764 - 4678 = 4086 \]

### Final Answer
The difference between the greatest and the smallest four-digit numbers formed by using the digits 8, 6, 7, and 4 is **4086**.

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