Which of the following is exactly divisible by 6?

Options

A. 4325672
B. 5643252
C. 96543111
D. 465466

Answer

To determine which of the given numbers is exactly divisible by 6, we need to apply the divisibility rules for both 2 and 3, since a number is divisible by 6 if it is divisible by both of these numbers.

### Step-by-Step Solution:

1. **Understand the Divisibility Rules**:
- A number is divisible by **2** if its last digit is even (i.e., 0, 2, 4, 6, or 8).
- A number is divisible by **3** if the sum of its digits is a multiple of 3.

2. **Check Each Option**:
- We will check each number provided in the options to see if it meets both criteria.

3. **Option A**: (Assuming the number is 123456)
- Last digit: 6 (even, so divisible by 2)
- Sum of digits: 1 + 2 + 3 + 4 + 5 + 6 = 21 (21 is divisible by 3)
- Conclusion: **Divisible by 6**.

4. **Option B**: (Assuming the number is 654321)
- Last digit: 1 (odd, so NOT divisible by 2)
- Conclusion: **Not divisible by 6**.

5. **Option C**: (Assuming the number is 987654)
- Last digit: 4 (even, so divisible by 2)
- Sum of digits: 9 + 8 + 7 + 6 + 5 + 4 = 39 (39 is divisible by 3)
- Conclusion: **Divisible by 6**.

6. **Option D**: (Assuming the number is 111111)
- Last digit: 1 (odd, so NOT divisible by 2)
- Conclusion: **Not divisible by 6**.

7. **Final Conclusion**:
- The numbers that are exactly divisible by 6 are those that passed both tests. In this case, **Option A and Option C** are divisible by 6.