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: #979691
⭐
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:
1. Fill in the blanks for each divisibility rule (based on standard math rules).
2. Use those rules to determine which numbers (in the “Divisibility Challenge”) are divisible by 2, 3, 4, 5, 6, 9, or 10 — and circle the correct factors.
---
## ✔ PART 1: FILL IN THE DIVISIBILITY RULES
Here are the completed rules with explanations:
| Rule # | Divisibility Rule | Examples (as given) |
|--------|-------------------------------------------------------------------------------------|----------------------|
| 1 | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, or 8). | 2, 4, 6, 8 |
| 2 | A number is divisible by 3 if the sum of the digits is divisible by 3. | 3 |
| 3 | A number is divisible by 4 if the last two digits form a number divisible by 4. | 4 |
| 4 | A number is divisible by 5 if the last digit is 0 or 5. | 5 |
| 5 | A number is divisible by 6 if it is divisible by both 2 and 3. | 6 |
| 6 | A number is divisible by 9 if the sum of the digits is divisible by 9. | 9 |
| 7 | A number is divisible by 10 if the last digit is 0. | 10 |
> 💡 Note: Rule #7 in the worksheet says “if the ___ of the digits is 0” — this is likely a typo or mislabeling. It should say “last digit is 0” for divisibility by 10. The phrase “sum of the digits is 0” only applies to the number 0 itself — so we’ll assume it’s meant to be “last digit”.
---
## ✔ PART 2: DIVISIBILITY CHALLENGE — CIRCLE THE FACTORS
We’ll go row by row, applying the rules above.
---
- Sum of digits: 5 + 7 = 12 → divisible by 3
- Last digit: 7 → not even → not divisible by 2, 5, 10
- Last two digits: 57 → 57 ÷ 4 = 14.25 → not divisible by 4
- Not divisible by 2 → not divisible by 6
- Sum 12 → not divisible by 9
✔ Divisible by: 3
---
- Even → divisible by 2
- Sum: 8+4=12 → divisible by 3 → also divisible by 6
- Last two digits: 84 → 84 ÷ 4 = 21 → divisible by 4
- Ends in 4 → not 0 or 5 → not divisible by 5 or 10
- Sum 12 → not divisible by 9
✔ Divisible by: 2, 3, 4, 6
---
- Even → divisible by 2
- Sum: 1+2+6=9 → divisible by 3 and 9 → also divisible by 6
- Last two digits: 26 → 26 ÷ 4 = 6.5 → not divisible by 4
- Ends in 6 → not 0 or 5 → not divisible by 5 or 10
✔ Divisible by: 2, 3, 6, 9
---
- Even → divisible by 2
- Sum: 2+3+0=5 → not divisible by 3 → not divisible by 6 or 9
- Last two digits: 30 → 30 ÷ 4 = 7.5 → not divisible by 4
- Ends in 0 → divisible by 5 and 10
✔ Divisible by: 2, 5, 10
---
- Even → divisible by 2
- Sum: 3+4+2=9 → divisible by 3 and 9 → also divisible by 6
- Last two digits: 42 → 42 ÷ 4 = 10.5 → not divisible by 4
- Ends in 2 → not 0 or 5 → not divisible by 5 or 10
✔ Divisible by: 2, 3, 6, 9
---
- Odd → not divisible by 2, 4, 6, 10
- Sum: 4+5+3=12 → divisible by 3
- Last digit: 3 → not 0 or 5 → not divisible by 5
- Sum 12 → not divisible by 9
✔ Divisible by: 3
---
- Even → divisible by 2
- Sum: 6+1+0=7 → not divisible by 3 → not divisible by 6 or 9
- Last two digits: 10 → 10 ÷ 4 = 2.5 → not divisible by 4
- Ends in 0 → divisible by 5 and 10
✔ Divisible by: 2, 5, 10
---
- Odd → not divisible by 2, 4, 6, 10
- Sum: 8+5+7=20 → not divisible by 3 or 9
- Last digit: 7 → not 0 or 5 → not divisible by 5
✔ Divisible by: none (only 1 and itself — prime)
---
- Even → divisible by 2
- Sum: 9+1+6=16 → not divisible by 3 → not divisible by 6 or 9
- Last two digits: 16 → 16 ÷ 4 = 4 → divisible by 4
- Ends in 6 → not 0 or 5 → not divisible by 5 or 10
✔ Divisible by: 2, 4
---
- Even → divisible by 2
- Sum: 2+0+5+8=15 → divisible by 3 → also divisible by 6
- Last two digits: 58 → 58 ÷ 4 = 14.5 → not divisible by 4
- Ends in 8 → not 0 or 5 → not divisible by 5 or 10
- Sum 15 → not divisible by 9
✔ Divisible by: 2, 3, 6
---
- Even → divisible by 2
- Sum: 8+6+1+6=21 → divisible by 3 → also divisible by 6
- Last two digits: 16 → 16 ÷ 4 = 4 → divisible by 4
- Ends in 6 → not 0 or 5 → not divisible by 5 or 10
- Sum 21 → not divisible by 9
✔ Divisible by: 2, 3, 4, 6
---
- Even → divisible by 2
- Sum: 7+3+2+6+0=18 → divisible by 3 and 9 → also divisible by 6
- Last two digits: 60 → 60 ÷ 4 = 15 → divisible by 4
- Ends in 0 → divisible by 5 and 10
✔ Divisible by: 2, 3, 4, 5, 6, 9, 10 ← All except possibly 7 (not tested here)
---
## 📝 FINAL ANSWER SUMMARY (CIRCLED FACTORS):
| 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 accordingly!
Let me know if you want a printable version or need help explaining any rule further!
1. Fill in the blanks for each divisibility rule (based on standard math rules).
2. Use those rules to determine which numbers (in the “Divisibility Challenge”) are divisible by 2, 3, 4, 5, 6, 9, or 10 — and circle the correct factors.
---
## ✔ PART 1: FILL IN THE DIVISIBILITY RULES
Here are the completed rules with explanations:
| Rule # | Divisibility Rule | Examples (as given) |
|--------|-------------------------------------------------------------------------------------|----------------------|
| 1 | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, or 8). | 2, 4, 6, 8 |
| 2 | A number is divisible by 3 if the sum of the digits is divisible by 3. | 3 |
| 3 | A number is divisible by 4 if the last two digits form a number divisible by 4. | 4 |
| 4 | A number is divisible by 5 if the last digit is 0 or 5. | 5 |
| 5 | A number is divisible by 6 if it is divisible by both 2 and 3. | 6 |
| 6 | A number is divisible by 9 if the sum of the digits is divisible by 9. | 9 |
| 7 | A number is divisible by 10 if the last digit is 0. | 10 |
> 💡 Note: Rule #7 in the worksheet says “if the ___ of the digits is 0” — this is likely a typo or mislabeling. It should say “last digit is 0” for divisibility by 10. The phrase “sum of the digits is 0” only applies to the number 0 itself — so we’ll assume it’s meant to be “last digit”.
---
## ✔ PART 2: DIVISIBILITY CHALLENGE — CIRCLE THE FACTORS
We’ll go row by row, applying the rules above.
---
🔢 57
- Sum of digits: 5 + 7 = 12 → divisible by 3
- Last digit: 7 → not even → not divisible by 2, 5, 10
- Last two digits: 57 → 57 ÷ 4 = 14.25 → not divisible by 4
- Not divisible by 2 → not divisible by 6
- Sum 12 → not divisible by 9
✔ Divisible by: 3
---
🔢 84
- Even → divisible by 2
- Sum: 8+4=12 → divisible by 3 → also divisible by 6
- Last two digits: 84 → 84 ÷ 4 = 21 → divisible by 4
- Ends in 4 → not 0 or 5 → not divisible by 5 or 10
- Sum 12 → not divisible by 9
✔ Divisible by: 2, 3, 4, 6
---
🔢 126
- Even → divisible by 2
- Sum: 1+2+6=9 → divisible by 3 and 9 → also divisible by 6
- Last two digits: 26 → 26 ÷ 4 = 6.5 → not divisible by 4
- Ends in 6 → not 0 or 5 → not divisible by 5 or 10
✔ Divisible by: 2, 3, 6, 9
---
🔢 230
- Even → divisible by 2
- Sum: 2+3+0=5 → not divisible by 3 → not divisible by 6 or 9
- Last two digits: 30 → 30 ÷ 4 = 7.5 → not divisible by 4
- Ends in 0 → divisible by 5 and 10
✔ Divisible by: 2, 5, 10
---
🔢 342
- Even → divisible by 2
- Sum: 3+4+2=9 → divisible by 3 and 9 → also divisible by 6
- Last two digits: 42 → 42 ÷ 4 = 10.5 → not divisible by 4
- Ends in 2 → not 0 or 5 → not divisible by 5 or 10
✔ Divisible by: 2, 3, 6, 9
---
🔢 453
- Odd → not divisible by 2, 4, 6, 10
- Sum: 4+5+3=12 → divisible by 3
- Last digit: 3 → not 0 or 5 → not divisible by 5
- Sum 12 → not divisible by 9
✔ Divisible by: 3
---
🔢 610
- Even → divisible by 2
- Sum: 6+1+0=7 → not divisible by 3 → not divisible by 6 or 9
- Last two digits: 10 → 10 ÷ 4 = 2.5 → not divisible by 4
- Ends in 0 → divisible by 5 and 10
✔ Divisible by: 2, 5, 10
---
🔢 857
- Odd → not divisible by 2, 4, 6, 10
- Sum: 8+5+7=20 → not divisible by 3 or 9
- Last digit: 7 → not 0 or 5 → not divisible by 5
✔ Divisible by: none (only 1 and itself — prime)
---
🔢 916
- Even → divisible by 2
- Sum: 9+1+6=16 → not divisible by 3 → not divisible by 6 or 9
- Last two digits: 16 → 16 ÷ 4 = 4 → divisible by 4
- Ends in 6 → not 0 or 5 → not divisible by 5 or 10
✔ Divisible by: 2, 4
---
🔢 2,058
- Even → divisible by 2
- Sum: 2+0+5+8=15 → divisible by 3 → also divisible by 6
- Last two digits: 58 → 58 ÷ 4 = 14.5 → not divisible by 4
- Ends in 8 → not 0 or 5 → not divisible by 5 or 10
- Sum 15 → not divisible by 9
✔ Divisible by: 2, 3, 6
---
🔢 8,616
- Even → divisible by 2
- Sum: 8+6+1+6=21 → divisible by 3 → also divisible by 6
- Last two digits: 16 → 16 ÷ 4 = 4 → divisible by 4
- Ends in 6 → not 0 or 5 → not divisible by 5 or 10
- Sum 21 → not divisible by 9
✔ Divisible by: 2, 3, 4, 6
---
🔢 73,260
- Even → divisible by 2
- Sum: 7+3+2+6+0=18 → divisible by 3 and 9 → also divisible by 6
- Last two digits: 60 → 60 ÷ 4 = 15 → divisible by 4
- Ends in 0 → divisible by 5 and 10
✔ Divisible by: 2, 3, 4, 5, 6, 9, 10 ← All except possibly 7 (not tested here)
---
## 📝 FINAL ANSWER SUMMARY (CIRCLED FACTORS):
| 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 accordingly!
Let me know if you want a printable version or need help explaining any rule further!
Parent Tip: Review the logic above to help your child master the concept of factors and divisibility worksheet.
