Using the tests of divisibility, find which of the following numbers are,
divisible by 6

Options

A. 24582
B. 35784
C. 24622
D. Both A & B

Answer

To determine which of the given numbers are divisible by 6, we will use the divisibility rules for both 2 and 3. A number is divisible by 6 if it is divisible by both 2 and 3.

### Step-by-Step Solution:

1. **Identify the Numbers**: The numbers we need to check are:
- 24582
- 357843
- 24622
- 723748

2. **Check Divisibility by 2**: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- **24582**: Last digit is 2 (even) → Divisible by 2.
- **357843**: Last digit is 3 (odd) → Not divisible by 2.
- **24622**: Last digit is 2 (even) → Divisible by 2.
- **723748**: Last digit is 8 (even) → 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 24582**:
- Sum of digits: 2 + 4 + 5 + 8 + 2 = 21
- 21 is divisible by 3 (21 ÷ 3 = 7) → Divisible by 3.
- **For 357843**:
- Sum of digits: 3 + 5 + 7 + 8 + 4 + 3 = 30
- 30 is divisible by 3 (30 ÷ 3 = 10) → Divisible by 3.
- **For 24622**:
- Sum of digits: 2 + 4 + 6 + 2 + 2 = 16
- 16 is not divisible by 3 (16 ÷ 3 = 5 remainder 1) → Not divisible by 3.
- **For 723748**:
- Sum of digits: 7 + 2 + 3 + 7 + 4 + 8 = 31
- 31 is not divisible by 3 (31 ÷ 3 = 10 remainder 1) → Not divisible by 3.

4. **Conclusion**:
- **24582**: Divisible by both 2 and 3 → Divisible by 6.
- **357843**: Divisible by both 2 and 3 → Divisible by 6.
- **24622**: Not divisible by 3 → Not divisible by 6.
- **723748**: Not divisible by 3 → Not divisible by 6.

### Final Results:
- **Divisible by 6**: 24582, 357843
- **Not Divisible by 6**: 24622, 723748