If `5x6 ` is three digit number exactly divisible by `3`, then the least value of `x` is

Options

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

Answer

To solve the problem, we need to find the least value of \( x \) such that the number \( 5x6 \) is exactly divisible by \( 3 \).

### Step-by-step Solution:

1. **Understanding the Number**: The number \( 5x6 \) represents a three-digit number where \( x \) is a digit (0-9).

2. **Divisibility Rule for 3**: A number is divisible by \( 3 \) if the sum of its digits is divisible by \( 3 \).

3. **Finding the Sum of the Digits**: The digits of the number \( 5x6 \) are \( 5 \), \( x \), and \( 6 \). Therefore, the sum of the digits is:
\[ 5 + x + 6 = 11 + x \]

4. **Setting Up the Condition for Divisibility**: We need \( 11 + x \) to be divisible by \( 3 \).

5. **Checking Values of \( x \)**: We will find the least value of \( x \) such that \( 11 + x \) is divisible by \( 3 \). We can check the values of \( x \) from \( 0 \) to \( 9 \):
- If \( x = 0 \): \( 11 + 0 = 11 \) (not divisible by 3)
- If \( x = 1 \): \( 11 + 1 = 12 \) (divisible by 3)
- If \( x = 2 \): \( 11 + 2 = 13 \) (not divisible by 3)
- If \( x = 3 \): \( 11 + 3 = 14 \) (not divisible by 3)
- If \( x = 4 \): \( 11 + 4 = 15 \) (divisible by 3)
- If \( x = 5 \): \( 11 + 5 = 16 \) (not divisible by 3)
- If \( x = 6 \): \( 11 + 6 = 17 \) (not divisible by 3)
- If \( x = 7 \): \( 11 + 7 = 18 \) (divisible by 3)
- If \( x = 8 \): \( 11 + 8 = 19 \) (not divisible by 3)
- If \( x = 9 \): \( 11 + 9 = 20 \) (not divisible by 3)

6. **Finding the Least Value**: From the checks above, the least value of \( x \) that makes \( 11 + x \) divisible by \( 3 \) is \( 1 \).

### Conclusion:
Thus, the least value of \( x \) is \( 1 \).

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