Divisibility Rule: Does Being Divisible by 9 Imply Divisibility by 3?

To solve this problem, we need to apply the divisibility rules for both 9 and 3.

• Step 1: Understand divisibility by 9.
  A number is divisible by 9 when the sum of its digits is a multiple of 9.
• Step 2: Understand divisibility by 3.
  A number is divisible by 3 when the sum of its digits is a multiple of 3.
• Step 3: Relate the rules.
  Since any multiple of 9 (given by the sum of digits) is also a multiple of 3, a number divisible by 9 is necessarily divisible by 3.

Therefore, it follows that if a number is divisible by 9, it must be divisible by 3, because the divisibility by 9 inherently satisfies the divisibility condition for 3.

Thus, the correct answer is Yes.