Which of the following numbers is divisible by 6 ?

Options

A. 67821
B. 78134
C. 87432
D. none of these

Answer

To determine which of the given numbers is divisible by 6, we need to follow these steps:

### Step-by-Step Solution:

1. **Understand the Divisibility Rule for 6**:
A number is divisible by 6 if it is divisible by both 2 and 3.

2. **Check the First Option: 6, 7, 8, 2, 1**:
- **Divisibility by 2**: Check the last digit. The last digit is 1, which is not even. Therefore, it is **not divisible by 2**.
- **Divisibility by 3**: Calculate the sum of the digits:
\(6 + 7 + 8 + 2 + 1 = 24\). Since \(24\) is divisible by \(3\), it is **divisible by 3**.
- Since it is not divisible by 2, **6, 7, 8, 2, 1 is not divisible by 6**.

3. **Check the Second Option: 7, 8, 1, 3, 4**:
- **Divisibility by 2**: The last digit is 4, which is even. Therefore, it is **divisible by 2**.
- **Divisibility by 3**: Calculate the sum of the digits:
\(7 + 8 + 1 + 3 + 4 = 23\). Since \(23\) is not divisible by \(3\), it is **not divisible by 3**.
- Since it is not divisible by 3, **7, 8, 1, 3, 4 is not divisible by 6**.

4. **Check the Third Option: 8, 7, 4, 3, 2**:
- **Divisibility by 2**: The last digit is 2, which is even. Therefore, it is **divisible by 2**.
- **Divisibility by 3**: Calculate the sum of the digits:
\(8 + 7 + 4 + 3 + 2 = 24\). Since \(24\) is divisible by \(3\), it is **divisible by 3**.
- Since it is divisible by both 2 and 3, **8, 7, 4, 3, 2 is divisible by 6**.

5. **Check the Fourth Option: None of These**:
- Since we found that **8, 7, 4, 3, 2** is divisible by 6, this option is not correct.

### Conclusion:
The number that is divisible by 6 from the given options is **8, 7, 4, 3, 2**.

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