See there that the divisibility rule of 4 is
If the last two digit number is divisible by 4 like such as 4632 this number having last digit 32 which is divisible by 4. 4245 this having kar digit 45 which is not divisible by 4.

Now the number is 1432 which is divisible by a 4.

Introduction:
To find the smallest 4-digit number divisible by 4 using the digits 1, 2, 3, and 4 only once, we need to understand the divisibility rule of 4 and apply it to the given digits.

Divisibility Rule of 4:
A number is divisible by 4 if the last two digits of the number form a multiple of 4. In other words, if the last two digits are divisible by 4, then the whole number is divisible by 4.

Analysis:
To find the smallest 4-digit number divisible by 4, we need to consider the possible combinations of the given digits and check if any of them satisfy the divisibility rule of 4.

Method:
1. Start by arranging the given digits in ascending order: 1, 2, 3, 4.
2. Since the number needs to be divisible by 4, the last two digits must form a multiple of 4.
3. The possible combinations for the last two digits are: 12, 14, 21, 24, 31, 34, 41, and 43.
4. We will check each combination starting from the smallest number, which is 12.
5. Since the first two digits need to be the remaining digits, we have two options: 34 and 41.
6. Let's check if the number formed by adding 12 at the end (1234 or 1243) is divisible by 4.
7. 1234 is not divisible by 4 since 34 is not a multiple of 4.
8. 1243 is also not divisible by 4 since 43 is not a multiple of 4.
9. We move on to the next combination, which is 14.
10. The remaining digits are 23 and 42.
11. Testing 1423 and 1442, we find that neither of them is divisible by 4.
12. We continue this process for the remaining combinations until we find a number that is divisible by 4.

Smallest 4-Digit Number Divisible by 4:
After testing all the combinations, we find that none of them satisfy the divisibility rule of 4.
Hence, there is no smallest 4-digit number that can be formed using the digits 1, 2, 3, and 4 only once, which is divisible by 4.