If 486*7 is exactly divisible by 9, then the least value of * is

Options

A. 0
B. 1
C. 3
D. 2

Answer

To solve the problem of finding the least value of * in the number 486*, where the entire number must be exactly divisible by 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the divisibility rule for 9**: A number is divisible by 9 if the sum of its digits is divisible by 9.

2. **Identify the digits of the number**: The number we have is 486*7. The digits are 4, 8, 6, *, and 7.

3. **Calculate the sum of the known digits**:
- Add the digits:
- 4 + 8 = 12
- 12 + 6 = 18
- 18 + 7 = 25
- So, the sum of the known digits is 25.

4. **Include the unknown digit * in the sum**:
- The total sum becomes 25 + *.

5. **Set up the condition for divisibility by 9**:
- We need (25 + *) to be divisible by 9.

6. **Find the smallest value of * that satisfies this condition**:
- Calculate the smallest multiple of 9 that is greater than or equal to 25. The multiples of 9 are 9, 18, 27, 36, etc. The smallest multiple of 9 that is greater than 25 is 27.
- Set up the equation:
- 25 + * = 27
- Solve for *:
- * = 27 - 25
- * = 2

7. **Conclusion**: The least value of * that makes the number 486*7 divisible by 9 is 2.

### Final Answer:
The least value of * is **2**.

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