Skill: Use divisibility rules for 3 and 9

To test whether a whole number is divisible by $3$ or $9$, add its digits.

• If the digit sum is divisible by $3$, the number is divisible by $3$.
• If the digit sum is divisible by $9$, the number is divisible by $9$.

Example: Is $(2{,}145)$ divisible by $3$ or $9$?

Step 1: Add the digits.

$$2+1+4+5=12$$

Step 2: Check $(12)$.

• $(12)$ is divisible by $3$, because $(12=3\times4)$.
• $(12)$ is not divisible by $9$.

Step 3: State the answer.

Therefore, $(2{,}145)$ is divisible by $3$, but it is not divisible by $9$.

Remember: Every number divisible by $9$ is also divisible by $3$, but a number divisible by $3$ is not always divisible by $9$.