The largest four digit even number that can be formed with the digits `0, 7, 3, 6` (without repetition) is

Options

A. `7036`
B. `0736`
C. `3067`
D. `7630`

Answer

To find the largest four-digit even number that can be formed with the digits 0, 7, 3, and 6 without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Even Digits**: The even digits from the given set are 0 and 6. Since we need to form an even number, the last digit of our four-digit number must be either 0 or 6.

2. **Case 1: Last Digit is 0**:
- If we choose 0 as the last digit, we need to arrange the remaining digits (7, 3, 6) in descending order to form the largest possible number.
- Arranging 7, 6, and 3 in descending order gives us 763.
- Therefore, if the last digit is 0, the largest number we can form is **7630**.

3. **Case 2: Last Digit is 6**:
- If we choose 6 as the last digit, we need to arrange the remaining digits (0, 7, 3) in descending order.
- Arranging 7, 3, and 0 in descending order gives us 730.
- Therefore, if the last digit is 6, the largest number we can form is **7306**.

4. **Compare the Two Cases**:
- From Case 1, we have 7630.
- From Case 2, we have 7306.
- Comparing these two numbers, **7630** is larger than **7306**.

5. **Conclusion**: The largest four-digit even number that can be formed with the digits 0, 7, 3, and 6 is **7630**.