Replace * by the smallest digit so that :
52*368 is divisible by 9

Options

A. `3`
B. `4`
C. `5
D. None of these

Answer

To solve the problem of replacing * in the number 52*368 with the smallest digit so that the entire number is divisible by 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rule of Divisibility by 9**: A number is divisible by 9 if the sum of its digits is divisible by 9.

2. **Identify the Digits in the Number**: The number we have is 52*368. The digits are 5, 2, *, 3, 6, and 8.

3. **Calculate the Sum of Known Digits**:
- Add the known digits together:
- 5 + 2 + 3 + 6 + 8 = 24

4. **Include the Unknown Digit**:
- Let the unknown digit (represented by *) be x.
- Therefore, the sum of the digits becomes:
- 24 + x

5. **Find the Smallest x for Divisibility by 9**:
- We need to find the smallest digit x (0 to 9) such that (24 + x) is divisible by 9.
- The multiples of 9 that are greater than or equal to 24 are 27, 36, etc.

6. **Calculate the Required x**:
- To make 24 + x = 27 (the next multiple of 9), we solve for x:
- 24 + x = 27
- x = 27 - 24
- x = 3

7. **Conclusion**:
- The smallest digit that can replace * is 3.
- Therefore, the number becomes 523368.

### Final Answer:
The required number is **523368**.