Divisibility Rules: Does Divisible by 9 Imply Divisible by 6?

To determine if a number divisible by 9 is necessarily divisible by 6, let's explore the divisibility rules.
A number is divisible by 9 if the sum of its digits is divisible by 9. Consequently, such a number is also divisible by 3 since divisibility by 9 implies divisibility by 3.
For divisibility by 6, a number must be divisible by both 2 and 3. We've established that a number divisible by 9 is also divisible by 3, so we now need to check whether it is necessarily divisible by 2.

Consider an example: the number 27 is divisible by 9 since $2 + 7 = 9$, which is divisible by 9. However, 27 is odd (since $27 \div 2 = 13.5$), and thus, not divisible by 2.
Since 27 is not divisible by both 2 and 3, this number is not divisible by 6.

Therefore, a number divisible by 9 is not necessarily divisible by 6. The correct answer is No.