Divisibility rules worksheet for 3,6 and 9 Worksheet - Free Printable

Problem Description:

The task is to determine whether each given number is divisible by 3, 6, or 9 using the divisibility rules. The numbers provided are:

- 12
- 30
- 72
- 18
- 54
- 81
- 66

We need to fill in a table with "Yes" or "No" for each number under the columns for 3, 6, and 9.

---

Divisibility Rules:

1. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisibility by 2: The last digit must be even (0, 2, 4, 6, or 8).
3. Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

---

Step-by-Step Solution:

#### Number: 12
- Divisibility by 3: Sum of digits = \(1 + 2 = 3\). Since 3 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 2 (even), and it is divisible by 3. So, Yes.
- Divisibility by 9: Sum of digits = \(1 + 2 = 3\). Since 3 is not divisible by 9, No.

#### Number: 30
- Divisibility by 3: Sum of digits = \(3 + 0 = 3\). Since 3 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 0 (even), and it is divisible by 3. So, Yes.
- Divisibility by 9: Sum of digits = \(3 + 0 = 3\). Since 3 is not divisible by 9, No.

#### Number: 72
- Divisibility by 3: Sum of digits = \(7 + 2 = 9\). Since 9 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 2 (even), and it is divisible by 3. So, Yes.
- Divisibility by 9: Sum of digits = \(7 + 2 = 9\). Since 9 is divisible by 9, Yes.

#### Number: 18
- Divisibility by 3: Sum of digits = \(1 + 8 = 9\). Since 9 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 8 (even), and it is divisible by 3. So, Yes.
- Divisibility by 9: Sum of digits = \(1 + 8 = 9\). Since 9 is divisible by 9, Yes.

#### Number: 54
- Divisibility by 3: Sum of digits = \(5 + 4 = 9\). Since 9 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 4 (even), and it is divisible by 3. So, Yes.
- Divisibility by 9: Sum of digits = \(5 + 4 = 9\). Since 9 is divisible by 9, Yes.

#### Number: 81
- Divisibility by 3: Sum of digits = \(8 + 1 = 9\). Since 9 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 1 (not even), so it is No.
- Divisibility by 9: Sum of digits = \(8 + 1 = 9\). Since 9 is divisible by 9, Yes.

#### Number: 66
- Divisibility by 3: Sum of digits = \(6 + 6 = 12\). Since 12 is divisible by 3, Yes.
- Divisibility by 6: Last digit is 6 (even), and it is divisible by 3. So, Yes.
- Divisibility by 9: Sum of digits = \(6 + 6 = 12\). Since 12 is not divisible by 9, No.

---

Final Answer:

The completed table is as follows:

| Number | 3 | 6 | 9 |
|--------|-----|-----|-----|
| 12 | Yes | Yes | No |
| 30 | Yes | Yes | No |
| 72 | Yes | Yes | Yes |
| 18 | Yes | Yes | Yes |
| 54 | Yes | Yes | Yes |
| 81 | Yes | No | Yes |
| 66 | Yes | Yes | No |

Thus, the final answer is:

\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\text{Number} & 3 & 6 & 9 \\
\hline
12 & \text{Yes} & \text{Yes} & \text{No} \\
30 & \text{Yes} & \text{Yes} & \text{No} \\
72 & \text{Yes} & \text{Yes} & \text{Yes} \\
18 & \text{Yes} & \text{Yes} & \text{Yes} \\
54 & \text{Yes} & \text{Yes} & \text{Yes} \\
81 & \text{Yes} & \text{No} & \text{Yes} \\
66 & \text{Yes} & \text{Yes} & \text{No} \\
\hline
\end{array}
}
\]