Divisibility Rules Worksheets - Free Printable
Educational worksheet: Divisibility Rules Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Divisibility Rules Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Divisibility Rules Worksheets
Let’s solve Challenge 1 first.
We are told:
- I am an even number → so the last digit must be 0, 2, 4, 6, or 8.
- I am divisible by 3 → sum of digits must be divisible by 3.
- One of my factors is 4 → that means the number must be divisible by 4. (Rule: last two digits form a number divisible by 4.)
- I am not divisible by 5 → so it cannot end in 0 or 5.
- Who am I? → We need to pick from A–H.
Let’s go through each option:
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A: 324
- Even? Yes (ends in 4) ✔
- Divisible by 3? 3+2+4 = 9 → yes ✔
- Divisible by 4? Last two digits: 24 → 24 ÷ 4 = 6 → yes ✔
- Not divisible by 5? Ends in 4 → yes ✔
→ So far, all clues match! But let’s check others to make sure only one fits.
---
B: 183
- Even? No (ends in 3) ✘ → eliminate
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C: 657
- Even? No (ends in 7) ✘ → eliminate
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D: 540
- Even? Yes ✔
- Divisible by 3? 5+4+0=9 → yes ✔
- Divisible by 4? Last two digits: 40 → 40÷4=10 → yes ✔
- Not divisible by 5? Ends in 0 → NO! It IS divisible by 5 → ✘ → eliminate
---
E: 245
- Even? No (ends in 5) ✘ → eliminate
---
F: 476
- Even? Yes ✔
- Divisible by 3? 4+7+6=17 → 17 not divisible by 3 → ✘ → eliminate
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G: 906
- Even? Yes ✔
- Divisible by 3? 9+0+6=15 → yes ✔
- Divisible by 4? Last two digits: 06 → 6 ÷ 4 = 1.5 → not divisible → ✘ → eliminate
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H: 751
- Even? No (ends in 1) ✘ → eliminate
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Only A: 324 satisfies ALL conditions.
✔ Final Answer for Challenge 1: A
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Now Challenge 2:
Clues:
- I am not divisible by 2 → so it’s odd → ends in 1, 3, 5, 7, 9
- I am not a multiple of 5 → so doesn’t end in 0 or 5
- I am divisible by 3 but not by 6 → divisible by 3, but since it’s not divisible by 2, it can’t be divisible by 6 anyway — this clue just confirms it’s odd and divisible by 3.
- One of my factors is 9 → so the number must be divisible by 9. (Rule: sum of digits divisible by 9)
- Who am I? → Pick from A–H again.
Go through options:
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A: 324
- Not divisible by 2? Ends in 4 → even → ✘ → eliminate
---
B: 183
- Odd? Yes ✔
- Not multiple of 5? Ends in 3 → yes ✔
- Divisible by 3? 1+8+3=12 → yes ✔
- Divisible by 9? 12 ÷ 9 = 1.33… → no → ✘ → eliminate
---
C: 657
- Odd? Yes ✔
- Not multiple of 5? Ends in 7 → yes ✔
- Divisible by 3? 6+5+7=18 → yes ✔
- Divisible by 9? 18 ÷ 9 = 2 → yes ✔
→ All clues satisfied! Let’s check others to be sure.
---
D: 540
- Odd? No → ends in 0 → ✘ → eliminate
---
E: 245
- Odd? Yes ✔
- Not multiple of 5? Ends in 5 → NO → ✘ → eliminate
---
F: 476
- Odd? No → ends in 6 → ✘ → eliminate
---
G: 906
- Odd? No → ends in 6 → ✘ → eliminate
---
H: 751
- Odd? Yes ✔
- Not multiple of 5? Ends in 1 → yes ✔
- Divisible by 3? 7+5+1=13 → not divisible by 3 → ✘ → eliminate
---
Only C: 657 satisfies all clues.
✔ Final Answer for Challenge 2: C
──────────────────────────────────────
Final Answer:
Challenge 1: A
Challenge 2: C
We are told:
- I am an even number → so the last digit must be 0, 2, 4, 6, or 8.
- I am divisible by 3 → sum of digits must be divisible by 3.
- One of my factors is 4 → that means the number must be divisible by 4. (Rule: last two digits form a number divisible by 4.)
- I am not divisible by 5 → so it cannot end in 0 or 5.
- Who am I? → We need to pick from A–H.
Let’s go through each option:
---
A: 324
- Even? Yes (ends in 4) ✔
- Divisible by 3? 3+2+4 = 9 → yes ✔
- Divisible by 4? Last two digits: 24 → 24 ÷ 4 = 6 → yes ✔
- Not divisible by 5? Ends in 4 → yes ✔
→ So far, all clues match! But let’s check others to make sure only one fits.
---
B: 183
- Even? No (ends in 3) ✘ → eliminate
---
C: 657
- Even? No (ends in 7) ✘ → eliminate
---
D: 540
- Even? Yes ✔
- Divisible by 3? 5+4+0=9 → yes ✔
- Divisible by 4? Last two digits: 40 → 40÷4=10 → yes ✔
- Not divisible by 5? Ends in 0 → NO! It IS divisible by 5 → ✘ → eliminate
---
E: 245
- Even? No (ends in 5) ✘ → eliminate
---
F: 476
- Even? Yes ✔
- Divisible by 3? 4+7+6=17 → 17 not divisible by 3 → ✘ → eliminate
---
G: 906
- Even? Yes ✔
- Divisible by 3? 9+0+6=15 → yes ✔
- Divisible by 4? Last two digits: 06 → 6 ÷ 4 = 1.5 → not divisible → ✘ → eliminate
---
H: 751
- Even? No (ends in 1) ✘ → eliminate
---
Only A: 324 satisfies ALL conditions.
✔ Final Answer for Challenge 1: A
---
Now Challenge 2:
Clues:
- I am not divisible by 2 → so it’s odd → ends in 1, 3, 5, 7, 9
- I am not a multiple of 5 → so doesn’t end in 0 or 5
- I am divisible by 3 but not by 6 → divisible by 3, but since it’s not divisible by 2, it can’t be divisible by 6 anyway — this clue just confirms it’s odd and divisible by 3.
- One of my factors is 9 → so the number must be divisible by 9. (Rule: sum of digits divisible by 9)
- Who am I? → Pick from A–H again.
Go through options:
---
A: 324
- Not divisible by 2? Ends in 4 → even → ✘ → eliminate
---
B: 183
- Odd? Yes ✔
- Not multiple of 5? Ends in 3 → yes ✔
- Divisible by 3? 1+8+3=12 → yes ✔
- Divisible by 9? 12 ÷ 9 = 1.33… → no → ✘ → eliminate
---
C: 657
- Odd? Yes ✔
- Not multiple of 5? Ends in 7 → yes ✔
- Divisible by 3? 6+5+7=18 → yes ✔
- Divisible by 9? 18 ÷ 9 = 2 → yes ✔
→ All clues satisfied! Let’s check others to be sure.
---
D: 540
- Odd? No → ends in 0 → ✘ → eliminate
---
E: 245
- Odd? Yes ✔
- Not multiple of 5? Ends in 5 → NO → ✘ → eliminate
---
F: 476
- Odd? No → ends in 6 → ✘ → eliminate
---
G: 906
- Odd? No → ends in 6 → ✘ → eliminate
---
H: 751
- Odd? Yes ✔
- Not multiple of 5? Ends in 1 → yes ✔
- Divisible by 3? 7+5+1=13 → not divisible by 3 → ✘ → eliminate
---
Only C: 657 satisfies all clues.
✔ Final Answer for Challenge 2: C
──────────────────────────────────────
Final Answer:
Challenge 1: A
Challenge 2: C
Parent Tip: Review the logic above to help your child master the concept of test of divisibility worksheet.
