Divisibility Rules: Is Every Multiple of 3 Also a Multiple of 6?

To determine if a number divisible by 3 is necessarily divisible by 6, we must apply the divisibility rules for both 3 and 6:

• A number is divisible by 3 if the sum of its digits is divisible by 3.
• A number is divisible by 6 if it is divisible by both 2 and 3. Thus, it must also be an even number.

To explore this question, let's consider a counterexample:

Take the number $9$. The sum of its digits is $9$, which is divisible by 3, so 9 is divisible by 3.

However, 9 is not even, so it is not divisible by 2. As a result, 9 is not divisible by 6 (because it does not satisfy the requirement to be divisible by both 2 and 3).

This counterexample demonstrates that a number divisible by 3 is not necessarily divisible by 6.

Therefore, the statement is incorrect, and the answer is No.