More Divisibility Rules Worksheets | Worsheets library - Free Printable
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Step-by-step solution for: More Divisibility Rules Worksheets | Worsheets library
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Show Answer Key & Explanations
Step-by-step solution for: More Divisibility Rules Worksheets | Worsheets library
Let’s go step by step to figure out which numbers each given number is divisible by (2, 3, 4, 5, 6, 9, or 10).
We’ll use simple divisibility rules:
- Divisible by 2? → Ends in even digit (0, 2, 4, 6, 8)
- Divisible by 3? → Sum of digits is divisible by 3
- Divisible by 4? → Last two digits form a number divisible by 4
- Divisible by 5? → Ends in 0 or 5
- Divisible by 6? → Divisible by BOTH 2 and 3
- Divisible by 9? → Sum of digits is divisible by 9
- Divisible by 10? → Ends in 0
Now let’s check each number one by one.
---
Number: 45
- Ends in 5 → Not divisible by 2 → ✘
- Sum = 4 + 5 = 9 → divisible by 3 → ✔
- Last two digits = 45 → 45 ÷ 4 = 11.25 → not divisible by 4 → ✘
- Ends in 5 → divisible by 5 → ✔
- Not divisible by 2 → so not by 6 → ✘
- Sum = 9 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 3, 5, 9
---
Number: 369
- Ends in 9 → odd → not divisible by 2 → ✘
- Sum = 3 + 6 + 9 = 18 → divisible by 3 → ✔
- Last two digits = 69 → 69 ÷ 4 = 17.25 → not divisible by 4 → ✘
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 2 → not by 6 → ✘
- Sum = 18 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 3, 9
---
Number: 7,870
- Ends in 0 → even → divisible by 2 → ✔
- Sum = 7+8+7+0 = 22 → 22 not divisible by 3 → ✘
- Last two digits = 70 → 70 ÷ 4 = 17.5 → not divisible by 4 → ✘
- Ends in 0 → divisible by 5 → ✔
- Not divisible by 3 → so not by 6 → ✘
- Sum = 22 → not divisible by 9 → ✘
- Ends in 0 → divisible by 10 → ✔
→ Checkmarks under: 2, 5, 10
---
Number: 1,976
- Ends in 6 → even → divisible by 2 → ✔
- Sum = 1+9+7+6 = 23 → not divisible by 3 → ✘
- Last two digits = 76 → 76 ÷ 4 = 19 → yes! → ✔
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 3 → so not by 6 → ✘
- Sum = 23 → not divisible by 9 → ✘
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 4
---
Number: 6,003
- Ends in 3 → odd → not divisible by 2 → ✘
- Sum = 6+0+0+3 = 9 → divisible by 3 → ✔
- Last two digits = 03 → 3 ÷ 4 = 0.75 → not divisible by 4 → ✘
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 2 → not by 6 → ✘
- Sum = 9 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 3, 9
---
Number: 136
- Ends in 6 → even → divisible by 2 → ✔
- Sum = 1+3+6 = 10 → not divisible by 3 → ✘
- Last two digits = 36 → 36 ÷ 4 = 9 → yes! → ✔
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 3 → so not by 6 → ✘
- Sum = 10 → not divisible by 9 → ✘
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 4
---
Number: 1,674
- Ends in 4 → even → divisible by 2 → ✔
- Sum = 1+6+7+4 = 18 → divisible by 3 → ✔
- Last two digits = 74 → 74 ÷ 4 = 18.5 → not divisible by 4 → ✘
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Divisible by 2 AND 3 → so divisible by 6 → ✔
- Sum = 18 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 3, 6, 9
---
Number: 35,496
- Ends in 6 → even → divisible by 2 → ✔
- Sum = 3+5+4+9+6 = 27 → divisible by 3 → ✔
- Last two digits = 96 → 96 ÷ 4 = 24 → yes! → ✔
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Divisible by 2 AND 3 → so divisible by 6 → ✔
- Sum = 27 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 3, 4, 6, 9
---
Final Answer:
For each number, place check marks under these columns:
- 45: 3, 5, 9
- 369: 3, 9
- 7,870: 2, 5, 10
- 1,976: 2, 4
- 6,003: 3, 9
- 136: 2, 4
- 1,674: 2, 3, 6, 9
- 35,496: 2, 3, 4, 6, 9
We’ll use simple divisibility rules:
- Divisible by 2? → Ends in even digit (0, 2, 4, 6, 8)
- Divisible by 3? → Sum of digits is divisible by 3
- Divisible by 4? → Last two digits form a number divisible by 4
- Divisible by 5? → Ends in 0 or 5
- Divisible by 6? → Divisible by BOTH 2 and 3
- Divisible by 9? → Sum of digits is divisible by 9
- Divisible by 10? → Ends in 0
Now let’s check each number one by one.
---
Number: 45
- Ends in 5 → Not divisible by 2 → ✘
- Sum = 4 + 5 = 9 → divisible by 3 → ✔
- Last two digits = 45 → 45 ÷ 4 = 11.25 → not divisible by 4 → ✘
- Ends in 5 → divisible by 5 → ✔
- Not divisible by 2 → so not by 6 → ✘
- Sum = 9 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 3, 5, 9
---
Number: 369
- Ends in 9 → odd → not divisible by 2 → ✘
- Sum = 3 + 6 + 9 = 18 → divisible by 3 → ✔
- Last two digits = 69 → 69 ÷ 4 = 17.25 → not divisible by 4 → ✘
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 2 → not by 6 → ✘
- Sum = 18 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 3, 9
---
Number: 7,870
- Ends in 0 → even → divisible by 2 → ✔
- Sum = 7+8+7+0 = 22 → 22 not divisible by 3 → ✘
- Last two digits = 70 → 70 ÷ 4 = 17.5 → not divisible by 4 → ✘
- Ends in 0 → divisible by 5 → ✔
- Not divisible by 3 → so not by 6 → ✘
- Sum = 22 → not divisible by 9 → ✘
- Ends in 0 → divisible by 10 → ✔
→ Checkmarks under: 2, 5, 10
---
Number: 1,976
- Ends in 6 → even → divisible by 2 → ✔
- Sum = 1+9+7+6 = 23 → not divisible by 3 → ✘
- Last two digits = 76 → 76 ÷ 4 = 19 → yes! → ✔
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 3 → so not by 6 → ✘
- Sum = 23 → not divisible by 9 → ✘
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 4
---
Number: 6,003
- Ends in 3 → odd → not divisible by 2 → ✘
- Sum = 6+0+0+3 = 9 → divisible by 3 → ✔
- Last two digits = 03 → 3 ÷ 4 = 0.75 → not divisible by 4 → ✘
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 2 → not by 6 → ✘
- Sum = 9 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 3, 9
---
Number: 136
- Ends in 6 → even → divisible by 2 → ✔
- Sum = 1+3+6 = 10 → not divisible by 3 → ✘
- Last two digits = 36 → 36 ÷ 4 = 9 → yes! → ✔
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Not divisible by 3 → so not by 6 → ✘
- Sum = 10 → not divisible by 9 → ✘
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 4
---
Number: 1,674
- Ends in 4 → even → divisible by 2 → ✔
- Sum = 1+6+7+4 = 18 → divisible by 3 → ✔
- Last two digits = 74 → 74 ÷ 4 = 18.5 → not divisible by 4 → ✘
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Divisible by 2 AND 3 → so divisible by 6 → ✔
- Sum = 18 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 3, 6, 9
---
Number: 35,496
- Ends in 6 → even → divisible by 2 → ✔
- Sum = 3+5+4+9+6 = 27 → divisible by 3 → ✔
- Last two digits = 96 → 96 ÷ 4 = 24 → yes! → ✔
- Doesn’t end in 0 or 5 → not divisible by 5 → ✘
- Divisible by 2 AND 3 → so divisible by 6 → ✔
- Sum = 27 → divisible by 9 → ✔
- Doesn’t end in 0 → not divisible by 10 → ✘
→ Checkmarks under: 2, 3, 4, 6, 9
---
Final Answer:
For each number, place check marks under these columns:
- 45: 3, 5, 9
- 369: 3, 9
- 7,870: 2, 5, 10
- 1,976: 2, 4
- 6,003: 3, 9
- 136: 2, 4
- 1,674: 2, 3, 6, 9
- 35,496: 2, 3, 4, 6, 9
Parent Tip: Review the logic above to help your child master the concept of divisibility rules worksheet 6th grade.
