Replace * by the smallest digit so that :
348 *02 is divisible by 6

Answer

To solve the problem of replacing * in the number 348*02 so that it is divisible by 6, we need to follow these steps:

### Step 1: Understand the divisibility rule for 6
A number is divisible by 6 if it is divisible by both 2 and 3.

### Step 2: Check divisibility by 2
A number is divisible by 2 if its last digit is even. In the number 348*02, the last digit is 2, which is even. Therefore, 348*02 is divisible by 2.

**Hint:** Check the last digit of the number to determine if it is even.

### Step 3: Check divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3. Let's calculate the sum of the digits in 348*02:

- The digits are 3, 4, 8, *, 0, and 2.
- The sum of the known digits is:
\[ 3 + 4 + 8 + 0 + 2 = 17 \]
- Now, we need to add the value of * to this sum:
\[ 17 + * \]

### Step 4: Find the smallest digit for *
We need to find the smallest digit (from 0 to 9) that can be added to 17 such that the total is divisible by 3.

Let's check each digit from 0 to 9:

- If * = 0: \( 17 + 0 = 17 \) (not divisible by 3)
- If * = 1: \( 17 + 1 = 18 \) (divisible by 3)
- If * = 2: \( 17 + 2 = 19 \) (not divisible by 3)
- If * = 3: \( 17 + 3 = 20 \) (not divisible by 3)
- If * = 4: \( 17 + 4 = 21 \) (divisible by 3)
- If * = 5: \( 17 + 5 = 22 \) (not divisible by 3)
- If * = 6: \( 17 + 6 = 23 \) (not divisible by 3)
- If * = 7: \( 17 + 7 = 24 \) (divisible by 3)
- If * = 8: \( 17 + 8 = 25 \) (not divisible by 3)
- If * = 9: \( 17 + 9 = 26 \) (not divisible by 3)

From the above checks, the smallest digit that makes the sum divisible by 3 is 1.

### Step 5: Replace * with 1
Thus, we replace * with 1 in the original number:
\[ 348*02 \rightarrow 348102 \]

### Final Answer
The required number is **348102**.

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