What smallest digit should be given to * so that 2315016* is divisible by 8?

Options

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

Answer

To determine the smallest digit that can replace the asterisk (*) in the number 2315016* so that the entire number is divisible by 8, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rule for Divisibility by 8**:
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

2. **Identify the Last Three Digits**:
The last three digits of the number 2315016* are 016*.

3. **Replace the Asterisk with Digits 0-9**:
We will test each digit from 0 to 9 to see which makes the number 016* divisible by 8.

4. **Test Each Digit**:
- For * = 0: The last three digits are 0160. Check if 160 is divisible by 8:
\[ 160 \div 8 = 20 \quad \text{(divisible)} \]
- For * = 1: The last three digits are 0161. Check if 161 is divisible by 8:
\[ 161 \div 8 = 20.125 \quad \text{(not divisible)} \]
- For * = 2: The last three digits are 0162. Check if 162 is divisible by 8:
\[ 162 \div 8 = 20.25 \quad \text{(not divisible)} \]
- For * = 3: The last three digits are 0163. Check if 163 is divisible by 8:
\[ 163 \div 8 = 20.375 \quad \text{(not divisible)} \]
- For * = 4: The last three digits are 0164. Check if 164 is divisible by 8:
\[ 164 \div 8 = 20.5 \quad \text{(not divisible)} \]
- For * = 5: The last three digits are 0165. Check if 165 is divisible by 8:
\[ 165 \div 8 = 20.625 \quad \text{(not divisible)} \]
- For * = 6: The last three digits are 0166. Check if 166 is divisible by 8:
\[ 166 \div 8 = 20.75 \quad \text{(not divisible)} \]
- For * = 7: The last three digits are 0167. Check if 167 is divisible by 8:
\[ 167 \div 8 = 20.875 \quad \text{(not divisible)} \]
- For * = 8: The last three digits are 0168. Check if 168 is divisible by 8:
\[ 168 \div 8 = 21 \quad \text{(divisible)} \]
- For * = 9: The last three digits are 0169. Check if 169 is divisible by 8:
\[ 169 \div 8 = 21.125 \quad \text{(not divisible)} \]

5. **Determine the Smallest Digit**:
From our tests, the digits that make the last three digits divisible by 8 are 0 and 8. The smallest digit is 0.

### Final Answer:
The smallest digit that should be given to * so that 2315016* is divisible by 8 is **0**.