Using digits 2,4,7 and 8 exactly once, find the smallest 4-digit number divisible by 4

Answer

To find the smallest 4-digit number using the digits 2, 4, 7, and 8 exactly once that is divisible by 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the divisibility rule for 4**: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

2. **List the digits**: The digits we have are 2, 4, 7, and 8.

3. **Start with the smallest digit**: Since we want the smallest 4-digit number, we should start with the smallest digit, which is 2.

4. **Form possible combinations**: We will form combinations of the digits starting with 2. The possible combinations with the remaining digits (4, 7, 8) are:
- 2478
- 2487
- 2748
- 2784
- 2847
- 2874

5. **Check divisibility by 4**: We need to check the last two digits of each combination to see if they are divisible by 4:
- For 2478, the last two digits are 78 (not divisible by 4)
- For 2487, the last two digits are 87 (not divisible by 4)
- For 2748, the last two digits are 48 (divisible by 4)
- For 2784, the last two digits are 84 (not divisible by 4)
- For 2847, the last two digits are 47 (not divisible by 4)
- For 2874, the last two digits are 74 (not divisible by 4)

6. **Identify the smallest valid combination**: The only combination that meets the criteria is 2748, as its last two digits (48) are divisible by 4.

### Final Answer:
The smallest 4-digit number that can be formed using the digits 2, 4, 7, and 8 exactly once and is divisible by 4 is **2748**.