Which of the following numbers is divisible by 6 ?

Options

A. 8790432
B. 98671402
C. 85492014
D. none of these

Answer

To determine which of the given numbers is divisible by 6, we need to check if each number is divisible by both 2 and 3.

**Step-by-step solution:**

1. **Identify the Numbers:**
We have the following numbers to check:
- Option 1: 8790432
- Option 2: 98671402
- Option 3: 85492014
- Option 4: None of these

2. **Check Divisibility by 2:**
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- For 8790432, the last digit is 2 (even), so it is divisible by 2.
- For 98671402, the last digit is 2 (even), so it is divisible by 2.
- For 85492014, the last digit is 4 (even), so it is divisible by 2.

3. **Check Divisibility by 3:**
A number is divisible by 3 if the sum of its digits is divisible by 3.
- For 8790432:
- Sum of digits: 8 + 7 + 9 + 0 + 4 + 3 + 2 = 33
- 33 ÷ 3 = 11 (divisible by 3)
- For 98671402:
- Sum of digits: 9 + 8 + 6 + 7 + 1 + 4 + 0 + 2 = 37
- 37 ÷ 3 = 12.33 (not divisible by 3)
- For 85492014:
- Sum of digits: 8 + 5 + 4 + 9 + 2 + 0 + 1 + 4 = 33
- 33 ÷ 3 = 11 (divisible by 3)

4. **Conclusion:**
- Option 1 (8790432) is divisible by both 2 and 3, hence it is divisible by 6.
- Option 2 (98671402) is not divisible by 3, hence it is not divisible by 6.
- Option 3 (85492014) is divisible by both 2 and 3, hence it is divisible by 6.
- Therefore, the numbers that are divisible by 6 are Option 1 and Option 3.

**Final Answer:**
Option 1 (8790432) and Option 3 (85492014) are divisible by 6.

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