Grade 5 Divisibility Rules Worksheet - Students mark check marks under numbers divisible by 2, 3, 5, 6, 9, and 10.
Divisibility rules worksheet for Grade 5 students, featuring a table to check divisibility by 2, 3, 5, 6, 9, and 10.
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Step-by-step solution for: Divisibility Rules interactive worksheet for Grade 5
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Show Answer Key & Explanations
Step-by-step solution for: Divisibility Rules interactive worksheet for Grade 5
To solve this problem, we need to determine which of the given numbers (2, 3, 5, 6, 9, and 10) each number on the left is divisible by. We will use the divisibility rules for each of these numbers:
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.
Now, let's analyze each number step by step:
---
- 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 5: Yes (last digit is 5).
- Divisible by 6: No (not divisible by 2).
- Divisible by 9: Yes (sum of digits = 4 + 5 = 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.
---
- 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 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 369: Check marks under 3 and 9.
---
- Divisible by 2: Yes (last digit is 0, which is even).
- Divisible by 3: No (sum of digits = 7 + 8 + 7 + 0 = 22, which 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, which is not divisible by 9).
- Divisible by 10: Yes (last digit is 0).
Result for 7,870: Check marks under 2, 5, and 10.
---
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: No (sum of digits = 1 + 9 + 7 + 6 = 23, which 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, which is not divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 1,976: Check mark under 2.
---
- 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 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 6,003: Check marks under 3 and 9.
---
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: No (sum of digits = 1 + 3 + 6 = 10, which 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, which is not divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 136: Check mark under 2.
---
- Divisible by 2: Yes (last digit is 4, which is even).
- Divisible by 3: Yes (sum of digits = 1 + 6 + 7 + 4 = 18, which 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 1,674: Check marks under 2, 3, 6, and 9.
---
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: Yes (sum of digits = 3 + 5 + 4 + 9 + 6 = 27, which 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 35,496: Check marks under 2, 3, 6, and 9.
---
\[
\boxed{
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Number} & \text{Divisible by 2} & \text{Divisible by 3} & \text{Divisible by 5} & \text{Divisible by 6} & \text{Divisible by 9} & \text{Divisible by 10} \\
\hline
45 & & \checkmark & \checkmark & & \checkmark & \\
\hline
369 & & \checkmark & & & \checkmark & \\
\hline
7,870 & \checkmark & & \checkmark & & & \checkmark \\
\hline
1,976 & \checkmark & & & & & \\
\hline
6,003 & & \checkmark & & & \checkmark & \\
\hline
136 & \checkmark & & & & & \\
\hline
1,674 & \checkmark & \checkmark & & \checkmark & \checkmark & \\
\hline
35,496 & \checkmark & \checkmark & & \checkmark & \checkmark & \\
\hline
\end{array}
}
\]
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.
Now, let's analyze each number step by step:
---
1. 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 5: Yes (last digit is 5).
- Divisible by 6: No (not divisible by 2).
- Divisible by 9: Yes (sum of digits = 4 + 5 = 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.
---
2. 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 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 369: Check marks under 3 and 9.
---
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, which 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, which is not divisible by 9).
- Divisible by 10: Yes (last digit is 0).
Result for 7,870: Check marks under 2, 5, and 10.
---
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, which 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, which is not divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 1,976: Check mark under 2.
---
5. 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 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 6,003: Check marks under 3 and 9.
---
6. 136
- Divisible by 2: Yes (last digit is 6, which is even).
- Divisible by 3: No (sum of digits = 1 + 3 + 6 = 10, which 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, which is not divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 136: Check mark under 2.
---
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, which 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 1,674: Check marks under 2, 3, 6, and 9.
---
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, which 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, which is divisible by 9).
- Divisible by 10: No (last digit is not 0).
Result for 35,496: Check marks under 2, 3, 6, and 9.
---
Final Answer:
\[
\boxed{
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Number} & \text{Divisible by 2} & \text{Divisible by 3} & \text{Divisible by 5} & \text{Divisible by 6} & \text{Divisible by 9} & \text{Divisible by 10} \\
\hline
45 & & \checkmark & \checkmark & & \checkmark & \\
\hline
369 & & \checkmark & & & \checkmark & \\
\hline
7,870 & \checkmark & & \checkmark & & & \checkmark \\
\hline
1,976 & \checkmark & & & & & \\
\hline
6,003 & & \checkmark & & & \checkmark & \\
\hline
136 & \checkmark & & & & & \\
\hline
1,674 & \checkmark & \checkmark & & \checkmark & \checkmark & \\
\hline
35,496 & \checkmark & \checkmark & & \checkmark & \checkmark & \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of divisibility rules practice worksheet.
