Explanations:To determine if a number is divisible by 3 or 9, we use the divisibility rules for these numbers. The rule for divisibility by 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. Similarly, a number is divisible by 9 if the sum of its digits is divisible by 9. These rules are based on the properties of the decimal number system, where each digit's place value is a power of 10, and 10 is congruent to 1 modulo 3 and 9.
Let's apply these rules to the given options:
For option A (810):
The sum of the digits is \(8 + 1 + 0 = 9\). Since 9 is divisible by both 3 and 9, 810 is divisible by both 3 and 9. Therefore, this option is incorrect.
For option B (270):
The sum of the digits is \(2 + 7 + 0 = 9\). Since 9 is divisible by both 3 and 9, 270 is divisible by both 3 and 9. Therefore, this option is incorrect.
For option C (330):
The sum of the digits is \(3 + 3 + 0 = 6\). Since 6 is divisible by 3 but not by 9, 330 is divisible by 3 but not by 9. Therefore, this option is correct.
For option D (450):
The sum of the digits is \(4 + 5 + 0 = 9\). Since 9 is divisible by both 3 and 9, 450 is divisible by both 3 and 9. Therefore, this option is incorrect.
Thus, the correct answer is 330, as it is divisible by 3 but not by 9.