Divisibility rules, Divisibility rules worksheet, Divisibility ... - Free Printable
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Step-by-step solution for: Divisibility rules, Divisibility rules worksheet, Divisibility ...
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Show Answer Key & Explanations
Step-by-step solution for: Divisibility rules, Divisibility rules worksheet, Divisibility ...
To solve the problem, we need to determine which of the given divisors (2, 3, 4, 5, 6, 7, 8, 9, 10) each number is divisible by. We will use the Rules of Divisibility for each divisor. Let's go through each number step by step.
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- Divisible by 2: The last digit is 2, which is even. Yes
- Divisible by 3: Sum of digits = \(4 + 3 + 2 = 9\). 9 is divisible by 3. Yes
- Divisible by 4: Last two digits are 32, and 32 ÷ 4 = 8. Yes
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Divisible by both 2 and 3. Yes
- Divisible by 7: Perform division: \(432 ÷ 7 ≈ 61.71\). Not an integer. No
- Divisible by 8: Last three digits are 432, and 432 ÷ 8 = 54. Yes
- Divisible by 9: Sum of digits = 9, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 432: Circle 2, 3, 4, 6, 8, 9
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- Divisible by 2: The last digit is 7, which is odd. No
- Divisible by 3: Sum of digits = \(3 + 5 + 7 = 15\). 15 is divisible by 3. Yes
- Divisible by 4: Last two digits are 57, and 57 ÷ 4 = 14.25. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 2. No
- Divisible by 7: Perform division: \(357 ÷ 7 = 51\). Yes
- Divisible by 8: Last three digits are 357, and 357 ÷ 8 = 44.625. No
- Divisible by 9: Sum of digits = 15, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 357: Circle 3, 7
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- Divisible by 2: The last digit is 0, which is even. Yes
- Divisible by 3: Sum of digits = \(2 + 3 + 6 + 0 = 11\). 11 is not divisible by 3. No
- Divisible by 4: Last two digits are 60, and 60 ÷ 4 = 15. Yes
- Divisible by 5: The last digit is 0. Yes
- Divisible by 6: Not divisible by 3. No
- Divisible by 7: Perform division: \(2360 ÷ 7 ≈ 337.14\). Not an integer. No
- Divisible by 8: Last three digits are 360, and 360 ÷ 8 = 45. Yes
- Divisible by 9: Sum of digits = 11, which is not divisible by 9. No
- Divisible by 10: The last digit is 0. Yes
Answer for 2,360: Circle 2, 4, 5, 8, 10
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- Divisible by 2: The last digit is 1, which is odd. No
- Divisible by 3: Sum of digits = \(5 + 6 + 7 + 1 = 19\). 19 is not divisible by 3. No
- Divisible by 4: Last two digits are 71, and 71 ÷ 4 = 17.75. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 2 or 3. No
- Divisible by 7: Perform division: \(5671 ÷ 7 ≈ 810.14\). Not an integer. No
- Divisible by 8: Last three digits are 671, and 671 ÷ 8 = 83.875. No
- Divisible by 9: Sum of digits = 19, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 5,671: None
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- Divisible by 2: The last digit is 3, which is odd. No
- Divisible by 3: Sum of digits = \(1 + 6 + 3 + 0 + 3 = 13\). 13 is not divisible by 3. No
- Divisible by 4: Last two digits are 03, and 03 ÷ 4 = 0.75. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 2 or 3. No
- Divisible by 7: Perform division: \(16303 ÷ 7 = 2329\). Yes
- Divisible by 8: Last three digits are 303, and 303 ÷ 8 = 37.875. No
- Divisible by 9: Sum of digits = 13, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 16,303: Circle 7
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- Divisible by 2: The last digit is 5, which is odd. No
- Divisible by 3: Sum of digits = \(3 + 8 + 4 + 7 + 5 = 27\). 27 is divisible by 3. Yes
- Divisible by 4: Last two digits are 75, and 75 ÷ 4 = 18.75. No
- Divisible by 5: The last digit is 5. Yes
- Divisible by 6: Not divisible by 2. No
- Divisible by 7: Perform division: \(38475 ÷ 7 ≈ 5496.43\). Not an integer. No
- Divisible by 8: Last three digits are 475, and 475 ÷ 8 = 59.375. No
- Divisible by 9: Sum of digits = 27, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 38,475: Circle 3, 5, 9
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- Divisible by 2: The last digit is 5, which is odd. No
- Divisible by 3: Sum of digits = \(4 + 0 + 0 + 0 + 0 + 5 = 9\). 9 is divisible by 3. Yes
- Divisible by 4: Last two digits are 05, and 05 ÷ 4 = 1.25. No
- Divisible by 5: The last digit is 5. Yes
- Divisible by 6: Not divisible by 2. No
- Divisible by 7: Perform division: \(400005 ÷ 7 ≈ 57143.57\). Not an integer. No
- Divisible by 8: Last three digits are 005, and 005 ÷ 8 = 0.625. No
- Divisible by 9: Sum of digits = 9, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 400,005: Circle 3, 5, 9
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- Divisible by 2: The last digit is 0, which is even. Yes
- Divisible by 3: Sum of digits = \(7 + 8 + 2 + 3 + 4 + 0 = 24\). 24 is divisible by 3. Yes
- Divisible by 4: Last two digits are 40, and 40 ÷ 4 = 10. Yes
- Divisible by 5: The last digit is 0. Yes
- Divisible by 6: Divisible by both 2 and 3. Yes
- Divisible by 7: Perform division: \(782340 ÷ 7 = 111762.857\). Not an integer. No
- Divisible by 8: Last three digits are 340, and 340 ÷ 8 = 42.5. No
- Divisible by 9: Sum of digits = 24, which is not divisible by 9. No
- Divisible by 10: The last digit is 0. Yes
Answer for 782,340: Circle 2, 3, 4, 5, 6, 10
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- Divisible by 2: The last digit is 4, which is even. Yes
- Divisible by 3: Sum of digits = \(7 + 3 + 2 + 1 + 6 + 9 + 4 = 32\). 32 is not divisible by 3. No
- Divisible by 4: Last two digits are 94, and 94 ÷ 4 = 23.5. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 3. No
- Divisible by 7: Perform division: \(7321694 ÷ 7 ≈ 1045956.29\). Not an integer. No
- Divisible by 8: Last three digits are 694, and 694 ÷ 8 = 86.75. No
- Divisible by 9: Sum of digits = 32, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 7,321,694: Circle 2
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- Divisible by 2: The last digit is 6, which is even. Yes
- Divisible by 3: Sum of digits = \(6 + 8 + 6 + 2 + 3 + 5 + 6 = 36\). 36 is divisible by 3. Yes
- Divisible by 4: Last two digits are 56, and 56 ÷ 4 = 14. Yes
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Divisible by both 2 and 3. Yes
- Divisible by 7: Perform division: \(6862356 ÷ 7 = 980336.571\). Not an integer. No
- Divisible by 8: Last three digits are 356, and 356 ÷ 8 = 44.5. No
- Divisible by 9: Sum of digits = 36, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 6,862,356: Circle 2, 3, 4, 6, 9
---
\[
\boxed{
\begin{array}{ll}
1. & 2, 3, 4, 6, 8, 9 \\
2. & 3, 7 \\
3. & 2, 4, 5, 8, 10 \\
4. & \text{None} \\
5. & 7 \\
6. & 3, 5, 9 \\
7. & 3, 5, 9 \\
8. & 2, 3, 4, 5, 6, 10 \\
9. & 2 \\
10. & 2, 3, 4, 6, 9 \\
\end{array}
}
\]
---
1. 432
- Divisible by 2: The last digit is 2, which is even. Yes
- Divisible by 3: Sum of digits = \(4 + 3 + 2 = 9\). 9 is divisible by 3. Yes
- Divisible by 4: Last two digits are 32, and 32 ÷ 4 = 8. Yes
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Divisible by both 2 and 3. Yes
- Divisible by 7: Perform division: \(432 ÷ 7 ≈ 61.71\). Not an integer. No
- Divisible by 8: Last three digits are 432, and 432 ÷ 8 = 54. Yes
- Divisible by 9: Sum of digits = 9, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 432: Circle 2, 3, 4, 6, 8, 9
---
2. 357
- Divisible by 2: The last digit is 7, which is odd. No
- Divisible by 3: Sum of digits = \(3 + 5 + 7 = 15\). 15 is divisible by 3. Yes
- Divisible by 4: Last two digits are 57, and 57 ÷ 4 = 14.25. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 2. No
- Divisible by 7: Perform division: \(357 ÷ 7 = 51\). Yes
- Divisible by 8: Last three digits are 357, and 357 ÷ 8 = 44.625. No
- Divisible by 9: Sum of digits = 15, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 357: Circle 3, 7
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3. 2,360
- Divisible by 2: The last digit is 0, which is even. Yes
- Divisible by 3: Sum of digits = \(2 + 3 + 6 + 0 = 11\). 11 is not divisible by 3. No
- Divisible by 4: Last two digits are 60, and 60 ÷ 4 = 15. Yes
- Divisible by 5: The last digit is 0. Yes
- Divisible by 6: Not divisible by 3. No
- Divisible by 7: Perform division: \(2360 ÷ 7 ≈ 337.14\). Not an integer. No
- Divisible by 8: Last three digits are 360, and 360 ÷ 8 = 45. Yes
- Divisible by 9: Sum of digits = 11, which is not divisible by 9. No
- Divisible by 10: The last digit is 0. Yes
Answer for 2,360: Circle 2, 4, 5, 8, 10
---
4. 5,671
- Divisible by 2: The last digit is 1, which is odd. No
- Divisible by 3: Sum of digits = \(5 + 6 + 7 + 1 = 19\). 19 is not divisible by 3. No
- Divisible by 4: Last two digits are 71, and 71 ÷ 4 = 17.75. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 2 or 3. No
- Divisible by 7: Perform division: \(5671 ÷ 7 ≈ 810.14\). Not an integer. No
- Divisible by 8: Last three digits are 671, and 671 ÷ 8 = 83.875. No
- Divisible by 9: Sum of digits = 19, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 5,671: None
---
5. 16,303
- Divisible by 2: The last digit is 3, which is odd. No
- Divisible by 3: Sum of digits = \(1 + 6 + 3 + 0 + 3 = 13\). 13 is not divisible by 3. No
- Divisible by 4: Last two digits are 03, and 03 ÷ 4 = 0.75. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 2 or 3. No
- Divisible by 7: Perform division: \(16303 ÷ 7 = 2329\). Yes
- Divisible by 8: Last three digits are 303, and 303 ÷ 8 = 37.875. No
- Divisible by 9: Sum of digits = 13, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 16,303: Circle 7
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6. 38,475
- Divisible by 2: The last digit is 5, which is odd. No
- Divisible by 3: Sum of digits = \(3 + 8 + 4 + 7 + 5 = 27\). 27 is divisible by 3. Yes
- Divisible by 4: Last two digits are 75, and 75 ÷ 4 = 18.75. No
- Divisible by 5: The last digit is 5. Yes
- Divisible by 6: Not divisible by 2. No
- Divisible by 7: Perform division: \(38475 ÷ 7 ≈ 5496.43\). Not an integer. No
- Divisible by 8: Last three digits are 475, and 475 ÷ 8 = 59.375. No
- Divisible by 9: Sum of digits = 27, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 38,475: Circle 3, 5, 9
---
7. 400,005
- Divisible by 2: The last digit is 5, which is odd. No
- Divisible by 3: Sum of digits = \(4 + 0 + 0 + 0 + 0 + 5 = 9\). 9 is divisible by 3. Yes
- Divisible by 4: Last two digits are 05, and 05 ÷ 4 = 1.25. No
- Divisible by 5: The last digit is 5. Yes
- Divisible by 6: Not divisible by 2. No
- Divisible by 7: Perform division: \(400005 ÷ 7 ≈ 57143.57\). Not an integer. No
- Divisible by 8: Last three digits are 005, and 005 ÷ 8 = 0.625. No
- Divisible by 9: Sum of digits = 9, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 400,005: Circle 3, 5, 9
---
8. 782,340
- Divisible by 2: The last digit is 0, which is even. Yes
- Divisible by 3: Sum of digits = \(7 + 8 + 2 + 3 + 4 + 0 = 24\). 24 is divisible by 3. Yes
- Divisible by 4: Last two digits are 40, and 40 ÷ 4 = 10. Yes
- Divisible by 5: The last digit is 0. Yes
- Divisible by 6: Divisible by both 2 and 3. Yes
- Divisible by 7: Perform division: \(782340 ÷ 7 = 111762.857\). Not an integer. No
- Divisible by 8: Last three digits are 340, and 340 ÷ 8 = 42.5. No
- Divisible by 9: Sum of digits = 24, which is not divisible by 9. No
- Divisible by 10: The last digit is 0. Yes
Answer for 782,340: Circle 2, 3, 4, 5, 6, 10
---
9. 7,321,694
- Divisible by 2: The last digit is 4, which is even. Yes
- Divisible by 3: Sum of digits = \(7 + 3 + 2 + 1 + 6 + 9 + 4 = 32\). 32 is not divisible by 3. No
- Divisible by 4: Last two digits are 94, and 94 ÷ 4 = 23.5. No
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Not divisible by 3. No
- Divisible by 7: Perform division: \(7321694 ÷ 7 ≈ 1045956.29\). Not an integer. No
- Divisible by 8: Last three digits are 694, and 694 ÷ 8 = 86.75. No
- Divisible by 9: Sum of digits = 32, which is not divisible by 9. No
- Divisible by 10: The last digit is not 0. No
Answer for 7,321,694: Circle 2
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10. 6,862,356
- Divisible by 2: The last digit is 6, which is even. Yes
- Divisible by 3: Sum of digits = \(6 + 8 + 6 + 2 + 3 + 5 + 6 = 36\). 36 is divisible by 3. Yes
- Divisible by 4: Last two digits are 56, and 56 ÷ 4 = 14. Yes
- Divisible by 5: The last digit is not 0 or 5. No
- Divisible by 6: Divisible by both 2 and 3. Yes
- Divisible by 7: Perform division: \(6862356 ÷ 7 = 980336.571\). Not an integer. No
- Divisible by 8: Last three digits are 356, and 356 ÷ 8 = 44.5. No
- Divisible by 9: Sum of digits = 36, which is divisible by 9. Yes
- Divisible by 10: The last digit is not 0. No
Answer for 6,862,356: Circle 2, 3, 4, 6, 9
---
Final Answer
\[
\boxed{
\begin{array}{ll}
1. & 2, 3, 4, 6, 8, 9 \\
2. & 3, 7 \\
3. & 2, 4, 5, 8, 10 \\
4. & \text{None} \\
5. & 7 \\
6. & 3, 5, 9 \\
7. & 3, 5, 9 \\
8. & 2, 3, 4, 5, 6, 10 \\
9. & 2 \\
10. & 2, 3, 4, 6, 9 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of divisibility rules practice worksheet.
