Divisibility rules worksheet for Grade 5 students to practice checking divisibility by 2, 3, 4, 5, 6, 9, and 10.

To solve the problem, we need to determine which of the given numbers are divisible by 2, 3, 4, 5, 6, 9, and 10. We will use the divisibility rules for each number:

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 4: The last two digits of the number must form a number divisible by 4.
4. Divisible by 5: The last digit must be 0 or 5.
5. Divisible by 6: The number must be divisible by both 2 and 3.
6. Divisible by 9: The sum of the digits of the number must be divisible by 9.
7. Divisible by 10: The last digit must be 0.

Now, let's analyze each number step by step:

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Number: 45

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

Result for 45: Check marks under 3, 5, and 9.

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Number: 369

- Divisible by 2: No (last digit is 9, not even).
- Divisible by 3: Yes (sum of digits = 3 + 6 + 9 = 18, which is divisible by 3).
- Divisible by 4: No (last two digits are 69, not divisible by 4).
- 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 = 18, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).

Result for 369: Check marks under 3 and 9.

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Number: 7,870

- Divisible by 2: Yes (last digit is 0, even).
- Divisible by 3: No (sum of digits = 7 + 8 + 7 + 0 = 22, not divisible by 3).
- Divisible by 4: Yes (last two digits are 70, and 70 ÷ 4 = 17.5, so no).
- Divisible by 5: Yes (last digit is 0).
- Divisible by 6: No (not divisible by 3).
- Divisible by 9: No (sum of digits = 22, not divisible by 9).
- Divisible by 10: Yes (last digit is 0).

Result for 7,870: Check marks under 2, 5, and 10.

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Number: 1,976

- Divisible by 2: Yes (last digit is 6, even).
- Divisible by 3: No (sum of digits = 1 + 9 + 7 + 6 = 23, not divisible by 3).
- Divisible by 4: Yes (last two digits are 76, and 76 ÷ 4 = 19).
- 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 = 23, not divisible by 9).
- Divisible by 10: No (last digit is not 0).

Result for 1,976: Check marks under 2 and 4.

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Number: 6,003

- Divisible by 2: No (last digit is 3, not even).
- Divisible by 3: Yes (sum of digits = 6 + 0 + 0 + 3 = 9, which is divisible by 3).
- Divisible by 4: No (last two digits are 03, not divisible by 4).
- 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 = 9, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).

Result for 6,003: Check marks under 3 and 9.

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Number: 136

- Divisible by 2: Yes (last digit is 6, even).
- Divisible by 3: No (sum of digits = 1 + 3 + 6 = 10, not divisible by 3).
- Divisible by 4: Yes (last two digits are 36, and 36 ÷ 4 = 9).
- 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 = 10, not divisible by 9).
- Divisible by 10: No (last digit is not 0).

Result for 136: Check marks under 2 and 4.

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Number: 1,674

- Divisible by 2: Yes (last digit is 4, even).
- Divisible by 3: Yes (sum of digits = 1 + 6 + 7 + 4 = 18, which is divisible by 3).
- Divisible by 4: Yes (last two digits are 74, and 74 ÷ 4 = 18.5, so no).
- 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 = 18, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).

Result for 1,674: Check marks under 2, 3, 4, 6, and 9.

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Number: 35,496

- Divisible by 2: Yes (last digit is 6, even).
- Divisible by 3: Yes (sum of digits = 3 + 5 + 4 + 9 + 6 = 27, which is divisible by 3).
- Divisible by 4: Yes (last two digits are 96, and 96 ÷ 4 = 24).
- 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 = 27, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).

Result for 35,496: Check marks under 2, 3, 4, 6, and 9.

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Final Answer:

\[
\boxed{
\begin{array}{c|ccccccc}
\text{Number} & \text{Divisible by?} \\
& 2 & 3 & 4 & 5 & 6 & 9 & 10 \\
\hline
45 & & \checkmark & & \checkmark & & \checkmark & \\
369 & & \checkmark & & & & \checkmark & \\
7,870 & \checkmark & & & \checkmark & & & \checkmark \\
1,976 & \checkmark & & \checkmark & & & & \\
6,003 & & \checkmark & & & & \checkmark & \\
136 & \checkmark & & \checkmark & & & & \\
1,674 & \checkmark & \checkmark & \checkmark & & \checkmark & \checkmark & \\
35,496 & \checkmark & \checkmark & \checkmark & & \checkmark & \checkmark & \\
\end{array}
}
\]