Consider the number 128436. Use divisibility tests to determine which of the numbers below a. factors of 128436. \( \begin{array}{lllllllllll}2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\end{array} \)

To determine which of the numbers are factors of 128436, we can use divisibility tests for each number. 1. **Divisibility by 2**: A number is divisible by 2 if its last digit is even. The last digit of 128436 is 6, which is even. **Conclusion**: 128436 is divisible by 2. 2. **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3. Sum of digits: \(1 + 2 + 8 + 4 + 3 + 6 = 24\). Since 24 is divisible by 3, **Conclusion**: 128436 is divisible by 3. 3. **Divisibility by 4**: A number is divisible by 4 if the last two digits form a number that is divisible by 4. The last two digits of 128436 are 36. \(36 \div 4 = 9\) (which is an integer). **Conclusion**: 128436 is divisible by 4. 4. **Divisibility by 5**: A number is divisible by 5 if its last digit is 0 or 5. The last digit of 128436 is 6. **Conclusion**: 128436 is not divisible by 5. 5. **Divisibility by 6**: A number is divisible by 6 if it is divisible by both 2 and 3. Since we have already established that 128436 is divisible by both 2 and 3, **Conclusion**: 128436 is divisible by 6. 6. **Divisibility by 7**: To check divisibility by 7, we can divide the number directly. \(128436 \div 7 \approx 18348\) (exact division). **Conclusion**: 128436 is divisible by 7. 7. **Divisibility by 8**: A number is divisible by 8 if the last three digits form a number that is divisible by 8. The last three digits of 128436 are 436. \(436 \div 8 = 54.5\) (not an integer). **Conclusion**: 128436 is not divisible by 8. 8. **Divisibility by 9**: A number is divisible by 9 if the sum of its digits is divisible by 9. We already calculated the sum of the digits as 24. \(24 \div 9 = 2.67\) (not an integer). **Conclusion**: 128436 is not divisible by 9. 9. **Divisibility by 10**: A number is divisible by 10 if its last digit is 0. The last digit of 128436 is 6. **Conclusion**: 128436 is not divisible by 10. 10. **Divisibility by 11**: To check divisibility by 11, we can use the alternating sum of the digits. Alternating sum: \(1 - 2 + 8 - 4 + 3 - 6 = 0\). Since 0 is divisible by 11, **Conclusion**: 128436 is divisible by 11. 11. **Divisibility by 12**: A number is divisible by 12 if it is divisible by both 3 and 4. Since we have established that 128436 is divisible by both 3 and 4, **Conclusion**: 128436 is divisible by 12. ### Summary of Results: - **Divisible by**: 2, 3, 4, 6, 7, 11, 12 - **Not divisible by**: 5, 8, 9, 10