Replace * by the smallest digit so that:
6238*8 is divisible by 4

Answer

To solve the problem of replacing * in the number 6238*8 so that it is divisible by 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Divisibility by 4**:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. In our case, the last two digits of the number 6238*8 are *8.

2. **Identifying the Last Two Digits**:
We need to replace * with a digit (0-9) to form the last two digits, which are *8.

3. **Testing Each Digit**:
We will test each digit from 0 to 9 to find the smallest digit that makes the number divisible by 4.

- **If * = 0**: The number becomes 623808. Check if 08 is divisible by 4.
- 08 ÷ 4 = 2 (divisible)

- **If * = 1**: The number becomes 623818. Check if 18 is divisible by 4.
- 18 ÷ 4 = 4.5 (not divisible)

- **If * = 2**: The number becomes 623828. Check if 28 is divisible by 4.
- 28 ÷ 4 = 7 (divisible)

- **If * = 3**: The number becomes 623838. Check if 38 is divisible by 4.
- 38 ÷ 4 = 9.5 (not divisible)

- **If * = 4**: The number becomes 623848. Check if 48 is divisible by 4.
- 48 ÷ 4 = 12 (divisible)

- **If * = 5**: The number becomes 623858. Check if 58 is divisible by 4.
- 58 ÷ 4 = 14.5 (not divisible)

- **If * = 6**: The number becomes 623868. Check if 68 is divisible by 4.
- 68 ÷ 4 = 17 (divisible)

- **If * = 7**: The number becomes 623878. Check if 78 is divisible by 4.
- 78 ÷ 4 = 19.5 (not divisible)

- **If * = 8**: The number becomes 623888. Check if 88 is divisible by 4.
- 88 ÷ 4 = 22 (divisible)

- **If * = 9**: The number becomes 623898. Check if 98 is divisible by 4.
- 98 ÷ 4 = 24.5 (not divisible)

4. **Finding the Smallest Digit**:
From our checks, the digits that made the number divisible by 4 are 0, 2, 4, 6, and 8. The smallest digit among these is **0**.

### Final Answer:
The smallest digit that can replace * in 6238*8 to make it divisible by 4 is **0**.