Grade 5 Divisibility Rules Worksheet - Practice checking divisibility by various numbers.

Problem Overview:

The task is to determine the divisibility of each given number by the numbers 2, 3, 5, 6, 9, and 10. We will use the divisibility rules for each of these numbers to solve the problem.

Divisibility Rules:

1. Divisible by 2: The number must be even (last digit is 0, 2, 4, 6, or 8).
2. Divisible by 3: The sum of the digits of the number must be divisible by 3.
3. Divisible by 5: The last digit must be 0 or 5.
4. Divisible by 6: The number must be divisible by both 2 and 3.
5. Divisible by 9: The sum of the digits of the number must be divisible by 9.
6. Divisible by 10: The last digit must be 0.

Numbers to Check:

The numbers provided are:
- 45
- 369
- 7,870
- 1,976
- 6,003
- 136
- 1,674
- 35,496

Step-by-Step Solution:

#### 1. 45
- Divisible by 2: No (last digit is 5, which is odd).
- Divisible by 3: Yes (sum of digits = 4 + 5 = 9, and 9 is divisible by 3).
- Divisible by 5: Yes (last digit is 5).
- Divisible by 6: No (not divisible by 2).
- Divisible by 9: Yes (sum of digits = 4 + 5 = 9, and 9 is divisible by 9).
- Divisible by 10: No (last digit is not 0).

#### 2. 369
- Divisible by 2: No (last digit is 9, which is odd).
- Divisible by 3: Yes (sum of digits = 3 + 6 + 9 = 18, and 18 is divisible by 3).
- Divisible by 5: No (last digit is not 0 or 5).
- Divisible by 6: No (not divisible by 2).
- Divisible by 9: Yes (sum of digits = 3 + 6 + 9 = 18, and 18 is divisible by 9).
- Divisible by 10: No (last digit is not 0).

#### 3. 7,870
- Divisible by 2: Yes (last digit is 0, which is even).
- Divisible by 3: No (sum of digits = 7 + 8 + 7 + 0 = 22, and 22 is not divisible by 3).
- Divisible by 5: Yes (last digit is 0).
- Divisible by 6: No (not divisible by 3).
- Divisible by 9: No (sum of digits = 7 + 8 + 7 + 0 = 22, and 22 is not divisible by 9).
- Divisible by 10: Yes (last digit is 0).

#### 4. 1,976
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: No (sum of digits = 1 + 9 + 7 + 6 = 23, and 23 is not divisible by 3).
- Divisible by 5: No (last digit is not 0 or 5).
- Divisible by 6: No (not divisible by 3).
- Divisible by 9: No (sum of digits = 1 + 9 + 7 + 6 = 23, and 23 is not divisible by 9).
- Divisible by 10: No (last digit is not 0).

#### 5. 6,003
- Divisible by 2: No (last digit is 3, which is odd).
- Divisible by 3: Yes (sum of digits = 6 + 0 + 0 + 3 = 9, and 9 is divisible by 3).
- Divisible by 5: No (last digit is not 0 or 5).
- Divisible by 6: No (not divisible by 2).
- Divisible by 9: Yes (sum of digits = 6 + 0 + 0 + 3 = 9, and 9 is divisible by 9).
- Divisible by 10: No (last digit is not 0).

#### 6. 136
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: No (sum of digits = 1 + 3 + 6 = 10, and 10 is not divisible by 3).
- Divisible by 5: No (last digit is not 0 or 5).
- Divisible by 6: No (not divisible by 3).
- Divisible by 9: No (sum of digits = 1 + 3 + 6 = 10, and 10 is not divisible by 9).
- Divisible by 10: No (last digit is not 0).

#### 7. 1,674
- Divisible by 2: Yes (last digit is 4, which is even).
- Divisible by 3: Yes (sum of digits = 1 + 6 + 7 + 4 = 18, and 18 is divisible by 3).
- Divisible by 5: No (last digit is not 0 or 5).
- Divisible by 6: Yes (divisible by both 2 and 3).
- Divisible by 9: Yes (sum of digits = 1 + 6 + 7 + 4 = 18, and 18 is divisible by 9).
- Divisible by 10: No (last digit is not 0).

#### 8. 35,496
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: Yes (sum of digits = 3 + 5 + 4 + 9 + 6 = 27, and 27 is divisible by 3).
- Divisible by 5: No (last digit is not 0 or 5).
- Divisible by 6: Yes (divisible by both 2 and 3).
- Divisible by 9: Yes (sum of digits = 3 + 5 + 4 + 9 + 6 = 27, and 27 is divisible by 9).
- Divisible by 10: No (last digit is not 0).

Final Answer:

We can summarize the results in a table format:

| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 6 | Divisible by 9 | Divisible by 10 |
|-----------|----------------|----------------|----------------|----------------|----------------|-----------------|
| 45 | No | Yes | Yes | No | Yes | No |
| 369 | No | Yes | No | No | Yes | No |
| 7,870 | Yes | No | Yes | No | No | Yes |
| 1,976 | Yes | No | No | No | No | No |
| 6,003 | No | Yes | No | No | Yes | No |
| 136 | Yes | No | No | No | No | No |
| 1,674 | Yes | Yes | No | Yes | Yes | No |
| 35,496 | Yes | Yes | No | Yes | Yes | No |

Thus, the final answer is:

\boxed{
\begin{array}{c|cccccc}
\text{Number} & \text{Divisible by 2} & \text{Divisible by 3} & \text{Divisible by 5} & \text{Divisible by 6} & \text{Divisible by 9} & \text{Divisible by 10} \\
\hline
45 & \text{No} & \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{No} \\
369 & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{No} \\
7,870 & \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{Yes} \\
1,976 & \text{Yes} & \text{No} & \text{No} & \text{No} & \text{No} & \text{No} \\
6,003 & \text{No} & \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{No} \\
136 & \text{Yes} & \text{No} & \text{No} & \text{No} & \text{No} & \text{No} \\
1,674 & \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{Yes} & \text{No} \\
35,496 & \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{Yes} & \text{No} \\
\end{array}
}