Learn About Divisibility Rules | Worksheet - Free Printable
Educational worksheet: Learn About Divisibility Rules | Worksheet. Download and print for classroom or home learning activities.
GIF
301×389
36.2 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1453224
⭐
Show Answer Key & Explanations
Step-by-step solution for: Learn About Divisibility Rules | Worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Learn About Divisibility Rules | Worksheet
You’re looking at a Divisibility Rules Worksheet from Education.com. The goal is to fill in the blanks for each divisibility rule and then apply those rules to determine which numbers (in the “Divisibility Challenge”) are divisible by 2, 3, 4, 5, 6, 9, or 10.
---
## ✔ PART 1: FILL IN THE DIVISIBILITY RULES
Here’s the correct completion of the table:
| # | Divisibility Rule | Examples |
|---|------------------------------------------------------------------------------------|------------------------------|
| 1 | A number is divisible by 1 if it is any whole number. | All numbers |
| 2 | If the last digit is even (0, 2, 4, 6, or 8), it is divisible by 2. | 24, 100, 58 |
| 3 | If the sum of the digits is divisible by 3, then the number is divisible by 3. | 123 → 1+2+3=6 → divisible by 3 |
| 4 | If the last two digits form a number divisible by 4, then the number is divisible by 4. | 124 → 24 ÷ 4 = 6 → yes |
| 5 | If the last digit is 0 or 5, then the number is divisible by 5. | 35, 70, 105 |
| 6 | If the number is divisible by both 2 and 3, then it is divisible by 6. | 12 → even & 1+2=3 → yes |
| 7 | *(Not required here — often skipped in elementary worksheets)* | — |
| 8 | If the last three digits form a number divisible by 8, then the number is divisible by 8. | 1024 → 024 ÷ 8 = 3 → yes |
| 9 | If the sum of the digits is divisible by 9, then the number is divisible by 9. | 189 → 1+8+9=18 → divisible |
| 10| If the last digit is 0, then the number is divisible by 10. | 50, 100, 230 |
> 💡 Note: Rule #1 is trivial — every whole number is divisible by 1. Sometimes it's omitted, but since it’s listed, we include it.
---
## ✔ PART 2: DIVISIBILITY CHALLENGE — APPLY THE RULES
We’ll go number by number and circle the factors it’s divisible by (from 2, 3, 4, 5, 6, 9, 10).
---
- Last digit = 7 → not even → ✘ 2
- Sum = 5+7 = 12 → divisible by 3 → ✔ 3
- Not divisible by 2 → ✘ 6
- Sum 12 not divisible by 9 → ✘ 9
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Last two digits = 57 → 57 ÷ 4 = 14.25 → ✘ 4
✔ Divisible by: 3
---
- Last digit = 4 → even → ✔ 2
- Sum = 8+4 = 12 → divisible by 3 → ✔ 3
- So also divisible by 6 → ✔ 6
- Last two digits = 84 → 84 ÷ 4 = 21 → ✔ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Sum 12 not divisible by 9 → ✘ 9
✔ Divisible by: 2, 3, 4, 6
---
- Last digit = 6 → even → ✔ 2
- Sum = 1+2+6 = 9 → divisible by 3 and 9 → ✔ 3, ✔ 9
- So also divisible by 6 → ✔ 6
- Last two digits = 26 → 26 ÷ 4 = 6.5 → ✘ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
✔ Divisible by: 2, 3, 6, 9
---
- Last digit = 0 → even → ✔ 2
- Also ends in 0 → ✔ 5, ✔ 10
- Sum = 2+3+0 = 5 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last two digits = 30 → 30 ÷ 4 = 7.5 → ✘ 4
✔ Divisible by: 2, 5, 10
---
- Last digit = 2 → even → ✔ 2
- Sum = 3+4+2 = 9 → divisible by 3 and 9 → ✔ 3, ✔ 9
- So also divisible by 6 → ✔ 6
- Last two digits = 42 → 42 ÷ 4 = 10.5 → ✘ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
✔ Divisible by: 2, 3, 6, 9
---
- Last digit = 3 → odd → ✘ 2
- Sum = 4+5+3 = 12 → divisible by 3 → ✔ 3
- Not divisible by 2 → ✘ 6
- Sum 12 not divisible by 9 → ✘ 9
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Last two digits = 53 → 53 ÷ 4 = 13.25 → ✘ 4
✔ Divisible by: 3
---
- Last digit = 0 → even → ✔ 2
- Also ends in 0 → ✔ 5, ✔ 10
- Sum = 6+1+0 = 7 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last two digits = 10 → 10 ÷ 4 = 2.5 → ✘ 4
✔ Divisible by: 2, 5, 10
---
- Last digit = 7 → odd → ✘ 2
- Sum = 8+5+7 = 20 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Last two digits = 57 → 57 ÷ 4 = 14.25 → ✘ 4
✔ Divisible by: NONE (only 1, but not listed)
→ So no circles
---
- Last digit = 6 → even → ✔ 2
- Sum = 9+1+6 = 16 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last two digits = 16 → 16 ÷ 4 = 4 → ✔ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
✔ Divisible by: 2, 4
---
- Last digit = 8 → even → ✔ 2
- Sum = 2+0+5+8 = 15 → divisible by 3 → ✔ 3
- So also divisible by 6 → ✔ 6
- Last two digits = 58 → 58 ÷ 4 = 14.5 → ✘ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Sum 15 not divisible by 9 → ✘ 9
✔ Divisible by: 2, 3, 6
---
- Last digit = 6 → even → ✔ 2
- Sum = 8+6+1+6 = 21 → divisible by 3 → ✔ 3
- So also divisible by 6 → ✔ 6
- Last two digits = 16 → 16 ÷ 4 = 4 → ✔ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Sum 21 not divisible by 9 → ✘ 9
✔ Divisible by: 2, 3, 4, 6
---
- Last digit = 0 → even → ✔ 2
- Also ends in 0 → ✔ 5, ✔ 10
- Sum = 7+3+2+6+0 = 18 → divisible by 3 and 9 → ✔ 3, ✔ 9
- So also divisible by 6 → ✔ 6
- Last two digits = 60 → 60 ÷ 4 = 15 → ✔ 4
✔ Divisible by: 2, 3, 4, 5, 6, 9, 10
---
## 🎯 FINAL ANSWER SUMMARY (CIRCLED FACTORS FOR EACH NUMBER)
| Number | Divisible by... |
|---------|------------------------------------------|
| 57 | 3 |
| 84 | 2, 3, 4, 6 |
| 126 | 2, 3, 6, 9 |
| 230 | 2, 5, 10 |
| 342 | 2, 3, 6, 9 |
| 453 | 3 |
| 610 | 2, 5, 10 |
| 857 | (none) |
| 916 | 2, 4 |
| 2,058 | 2, 3, 6 |
| 8,616 | 2, 3, 4, 6 |
| 73,260 | 2, 3, 4, 5, 6, 9, 10 |
---
✔ You can now fill in the worksheet with these answers!
Let me know if you’d like a printable version or want to check your own work!
---
## ✔ PART 1: FILL IN THE DIVISIBILITY RULES
Here’s the correct completion of the table:
| # | Divisibility Rule | Examples |
|---|------------------------------------------------------------------------------------|------------------------------|
| 1 | A number is divisible by 1 if it is any whole number. | All numbers |
| 2 | If the last digit is even (0, 2, 4, 6, or 8), it is divisible by 2. | 24, 100, 58 |
| 3 | If the sum of the digits is divisible by 3, then the number is divisible by 3. | 123 → 1+2+3=6 → divisible by 3 |
| 4 | If the last two digits form a number divisible by 4, then the number is divisible by 4. | 124 → 24 ÷ 4 = 6 → yes |
| 5 | If the last digit is 0 or 5, then the number is divisible by 5. | 35, 70, 105 |
| 6 | If the number is divisible by both 2 and 3, then it is divisible by 6. | 12 → even & 1+2=3 → yes |
| 7 | *(Not required here — often skipped in elementary worksheets)* | — |
| 8 | If the last three digits form a number divisible by 8, then the number is divisible by 8. | 1024 → 024 ÷ 8 = 3 → yes |
| 9 | If the sum of the digits is divisible by 9, then the number is divisible by 9. | 189 → 1+8+9=18 → divisible |
| 10| If the last digit is 0, then the number is divisible by 10. | 50, 100, 230 |
> 💡 Note: Rule #1 is trivial — every whole number is divisible by 1. Sometimes it's omitted, but since it’s listed, we include it.
---
## ✔ PART 2: DIVISIBILITY CHALLENGE — APPLY THE RULES
We’ll go number by number and circle the factors it’s divisible by (from 2, 3, 4, 5, 6, 9, 10).
---
🔢 57
- Last digit = 7 → not even → ✘ 2
- Sum = 5+7 = 12 → divisible by 3 → ✔ 3
- Not divisible by 2 → ✘ 6
- Sum 12 not divisible by 9 → ✘ 9
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Last two digits = 57 → 57 ÷ 4 = 14.25 → ✘ 4
✔ Divisible by: 3
---
🔢 84
- Last digit = 4 → even → ✔ 2
- Sum = 8+4 = 12 → divisible by 3 → ✔ 3
- So also divisible by 6 → ✔ 6
- Last two digits = 84 → 84 ÷ 4 = 21 → ✔ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Sum 12 not divisible by 9 → ✘ 9
✔ Divisible by: 2, 3, 4, 6
---
🔢 126
- Last digit = 6 → even → ✔ 2
- Sum = 1+2+6 = 9 → divisible by 3 and 9 → ✔ 3, ✔ 9
- So also divisible by 6 → ✔ 6
- Last two digits = 26 → 26 ÷ 4 = 6.5 → ✘ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
✔ Divisible by: 2, 3, 6, 9
---
🔢 230
- Last digit = 0 → even → ✔ 2
- Also ends in 0 → ✔ 5, ✔ 10
- Sum = 2+3+0 = 5 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last two digits = 30 → 30 ÷ 4 = 7.5 → ✘ 4
✔ Divisible by: 2, 5, 10
---
🔢 342
- Last digit = 2 → even → ✔ 2
- Sum = 3+4+2 = 9 → divisible by 3 and 9 → ✔ 3, ✔ 9
- So also divisible by 6 → ✔ 6
- Last two digits = 42 → 42 ÷ 4 = 10.5 → ✘ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
✔ Divisible by: 2, 3, 6, 9
---
🔢 453
- Last digit = 3 → odd → ✘ 2
- Sum = 4+5+3 = 12 → divisible by 3 → ✔ 3
- Not divisible by 2 → ✘ 6
- Sum 12 not divisible by 9 → ✘ 9
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Last two digits = 53 → 53 ÷ 4 = 13.25 → ✘ 4
✔ Divisible by: 3
---
🔢 610
- Last digit = 0 → even → ✔ 2
- Also ends in 0 → ✔ 5, ✔ 10
- Sum = 6+1+0 = 7 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last two digits = 10 → 10 ÷ 4 = 2.5 → ✘ 4
✔ Divisible by: 2, 5, 10
---
🔢 857
- Last digit = 7 → odd → ✘ 2
- Sum = 8+5+7 = 20 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Last two digits = 57 → 57 ÷ 4 = 14.25 → ✘ 4
✔ Divisible by: NONE (only 1, but not listed)
→ So no circles
---
🔢 916
- Last digit = 6 → even → ✔ 2
- Sum = 9+1+6 = 16 → not divisible by 3 → ✘ 3, ✘ 6, ✘ 9
- Last two digits = 16 → 16 ÷ 4 = 4 → ✔ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
✔ Divisible by: 2, 4
---
🔢 2,058
- Last digit = 8 → even → ✔ 2
- Sum = 2+0+5+8 = 15 → divisible by 3 → ✔ 3
- So also divisible by 6 → ✔ 6
- Last two digits = 58 → 58 ÷ 4 = 14.5 → ✘ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Sum 15 not divisible by 9 → ✘ 9
✔ Divisible by: 2, 3, 6
---
🔢 8,616
- Last digit = 6 → even → ✔ 2
- Sum = 8+6+1+6 = 21 → divisible by 3 → ✔ 3
- So also divisible by 6 → ✔ 6
- Last two digits = 16 → 16 ÷ 4 = 4 → ✔ 4
- Last digit ≠ 0 or 5 → ✘ 5, ✘ 10
- Sum 21 not divisible by 9 → ✘ 9
✔ Divisible by: 2, 3, 4, 6
---
🔢 73,260
- Last digit = 0 → even → ✔ 2
- Also ends in 0 → ✔ 5, ✔ 10
- Sum = 7+3+2+6+0 = 18 → divisible by 3 and 9 → ✔ 3, ✔ 9
- So also divisible by 6 → ✔ 6
- Last two digits = 60 → 60 ÷ 4 = 15 → ✔ 4
✔ Divisible by: 2, 3, 4, 5, 6, 9, 10
---
## 🎯 FINAL ANSWER SUMMARY (CIRCLED FACTORS FOR EACH NUMBER)
| Number | Divisible by... |
|---------|------------------------------------------|
| 57 | 3 |
| 84 | 2, 3, 4, 6 |
| 126 | 2, 3, 6, 9 |
| 230 | 2, 5, 10 |
| 342 | 2, 3, 6, 9 |
| 453 | 3 |
| 610 | 2, 5, 10 |
| 857 | (none) |
| 916 | 2, 4 |
| 2,058 | 2, 3, 6 |
| 8,616 | 2, 3, 4, 6 |
| 73,260 | 2, 3, 4, 5, 6, 9, 10 |
---
✔ You can now fill in the worksheet with these answers!
Let me know if you’d like a printable version or want to check your own work!
Parent Tip: Review the logic above to help your child master the concept of divisibility worksheet.
