Find the difference between the largest 7-digit number and the smallest 7-digit number formed by using the digits 4, 0, 3, 9 and 7 (using each digit at least once).

Options

A. 6993951
B. 6949530
C. 6963951
D. 6996951

Answer

To solve the problem of finding the difference between the largest 7-digit number and the smallest 7-digit number formed by using the digits 4, 0, 3, 9, and 7 (with each digit used at least once), we can follow these steps:

### Step 1: Identify the digits available
The digits we have are 4, 0, 3, 9, and 7.

### Step 2: Form the largest 7-digit number
To create the largest 7-digit number, we should arrange the digits in descending order. Since we need a 7-digit number and we have only 5 unique digits, we can repeat some of the digits.

1. Start with the largest digit, which is 9.
2. Next, use 7, then 4, then 3, and finally 0.
3. To maximize the number, we can repeat the largest digits. Thus, we can form the number as follows:
- Use 9 three times, 7 two times, and 4, 3, and 0 once each.

So, the largest 7-digit number is:
**9997443**

### Step 3: Form the smallest 7-digit number
To create the smallest 7-digit number, we should arrange the digits in ascending order. However, we cannot start with 0, as it would not be a valid 7-digit number.

1. Start with the smallest non-zero digit, which is 3.
2. Then use 0, and repeat the smallest digits to fill the remaining places.
3. The arrangement can be:
- Use 3 once, 0 three times, and then 4 and 7.

So, the smallest 7-digit number is:
**3000047**

### Step 4: Calculate the difference
Now we need to find the difference between the largest and smallest 7-digit numbers:
- Largest number: 9997443
- Smallest number: 3000047

Performing the subtraction:
```
9997443
- 3000047
___________
6997396
```

### Final Answer
The difference between the largest 7-digit number and the smallest 7-digit number is **6997396**.

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