Final answer:
Applying divisibility rules shows that 1044 is divisible by 2, 3, and 6, but not by 5, 9, or 10. 1485 is divisible by 3, 5, and 9, but not by 2, 6, or 10. 1620 is divisible by all except 9, and 1709 is not divisible by any of the given numbers.
Step-by-step explanation:
To determine whether the numbers 1044, 1485, 1620, and 1709 are divisible by 2, 3, 5, 6, 9, and 10, we can use the following divisibility rules:
- Divisible by 2: A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
- Divisible by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisible by 5: A number is divisible by 5 if its last digit is 0 or 5.
- Divisible by 6: A number is divisible by 6 if it's divisible by both 2 and 3.
- Divisible by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- Divisible by 10: A number is divisible by 10 if its last digit is 0.
Applying these rules:
- 1044 is even, so it's divisible by 2. The sum of its digits is 1+0+4+4 = 9, which is divisible by 3, so it's also divisible by 3 and consequently by 6. It's not divisible by 5, 9, or 10.
- 1485 ends with 5, so it's divisible by 5. The sum of its digits is 1+4+8+5 = 18, which is divisible by both 3 and 9. It's not divisible by 2, 6, or 10.
- 1620 ends with a 0, so it's divisible by 2, 5, and 10. The sum of its digits is 1+6+2+0 = 9, which is divisible by 3 and 9. It's also divisible by 6 as it meets the criteria for divisibility by both 2 and 3.
- 1709 is not divisible by 2, 3, 5, 6, 9, or 10.
Therefore, the correct answer is a) 1044: Yes, 1485: Yes, 1620: Yes, 1709: No.