To determine which of the following numbers is divisible by 2, 4, 6, and 8, we need to analyze the divisibility rules for each of these numbers.
### Step-by-Step Solution:
1. **Understanding Divisibility Rules**:
- A number is divisible by **2** if its last digit is even (0, 2, 4, 6, 8).
- A number is divisible by **4** if the last two digits form a number that is divisible by 4.
- A number is divisible by **6** if it is divisible by both 2 and 3. For divisibility by 3, the sum of the digits must be divisible by 3.
- A number is divisible by **8** if the last three digits form a number that is divisible by 8.
2. **Identifying the Options**:
- Let's assume the options are: 2, 4, 6, and 8 (as per the question).
- We will check each option for divisibility by 2, 4, 6, and 8.
3. **Checking Each Option**:
- **Option 1: 2**
- Divisible by 2: Yes (last digit is 2).
- Divisible by 4: No (2 is not divisible by 4).
- Divisible by 6: No (not divisible by 3).
- Divisible by 8: No (2 is not divisible by 8).
- **Conclusion**: Not divisible by all.
- **Option 2: 4**
- Divisible by 2: Yes (last digit is 4).
- Divisible by 4: Yes (4 is divisible by 4).
- Divisible by 6: No (not divisible by 3).
- Divisible by 8: No (4 is not divisible by 8).
- **Conclusion**: Not divisible by all.
- **Option 3: 6**
- Divisible by 2: Yes (last digit is 6).
- Divisible by 4: No (6 is not divisible by 4).
- Divisible by 6: Yes (itself).
- Divisible by 8: No (6 is not divisible by 8).
- **Conclusion**: Not divisible by all.
- **Option 4: 8**
- Divisible by 2: Yes (last digit is 8).
- Divisible by 4: Yes (8 is divisible by 4).
- Divisible by 6: No (not divisible by 3).
- Divisible by 8: Yes (itself).
- **Conclusion**: Not divisible by all.
4. **Final Conclusion**:
- None of the options (2, 4, 6, 8) are divisible by all of 2, 4, 6, and 8.
