Find the difference between the greatest 5-digit number and the greatest 4-digit number formed using the digits 7, 6, 2, 5, 1 when the repetition is not allowed.

Explanation

To find the difference between the greatest 5-digit number and the greatest 4-digit number formed using the digits 7, 6, 2, 5, and 1 without repetition, we can follow these steps:

### Step 1: Identify the digits
The digits we have are 7, 6, 2, 5, and 1.

### Step 2: Form the greatest 5-digit number
To form the greatest 5-digit number, we need to arrange the digits in descending order.
- The digits in descending order are: 7, 6, 5, 2, 1.
- Therefore, the greatest 5-digit number is **76521**.

### Step 3: Form the greatest 4-digit number
Next, we need to form the greatest 4-digit number using the same digits.
- We again arrange the digits in descending order, but this time we will use only the first four digits: 7, 6, 5, and 2.
- Therefore, the greatest 4-digit number is **7652**.

### Step 4: Calculate the difference
Now we will subtract the greatest 4-digit number from the greatest 5-digit number.
- The calculation is:
\[ 76521 - 7652 \]

### Step 5: Perform the subtraction
Let's perform the subtraction:
- Align the numbers:
```
76521
- 7652
-------
```
- Subtract from right to left:
- 1 - 2 = 9 (borrow 1 from the next digit)
- 2 - 5 = 7 (after borrowing, it becomes 12 - 5)
- 5 - 6 = 8 (after borrowing, it becomes 15 - 6)
- 6 - 7 = 8 (after borrowing, it becomes 16 - 7)
- 7 - 0 = 7

So, the result is **68869**.

### Final Answer
The difference between the greatest 5-digit number and the greatest 4-digit number is **68869**.

---