Let's solve the problem step by step. The task is to
express each number as a product of its prime factors.
We'll go through each number one by one, using
prime factorization (breaking down the number into its prime components).
---
🔢 1. 55
- Divide by the smallest prime: 5 → 55 ÷ 5 = 11
- 11 is a prime number.
- So,
55 = 5 × 11
✔ Prime factors:
5 × 11
---
🔢 2. 105
- Divide by 5 → 105 ÷ 5 = 21
- 21 = 3 × 7
- So,
105 = 5 × 3 × 7
✔ Prime factors:
3 × 5 × 7
---
🔢 3. 260
- Divide by 2 → 260 ÷ 2 = 130
- 130 ÷ 2 = 65
- 65 ÷ 5 = 13
- 13 is prime
- So,
260 = 2 × 2 × 5 × 13 = 2² × 5 × 13
✔ Prime factors:
2 × 2 × 5 × 13
---
🔢 4. 390
- Divide by 2 → 390 ÷ 2 = 195
- 195 ÷ 3 = 65
- 65 ÷ 5 = 13
- 13 is prime
- So,
390 = 2 × 3 × 5 × 13
✔ Prime factors:
2 × 3 × 5 × 13
---
🔢 5. 882
- Divide by 2 → 882 ÷ 2 = 441
- 441 ÷ 3 = 147
- 147 ÷ 3 = 49
- 49 = 7 × 7
- So,
882 = 2 × 3 × 3 × 7 × 7 = 2 × 3² × 7²
✔ Prime factors:
2 × 3 × 3 × 7 × 7
---
🔢 6. 396
- Divide by 2 → 396 ÷ 2 = 198
- 198 ÷ 2 = 99
- 99 ÷ 3 = 33
- 33 ÷ 3 = 11
- 11 is prime
- So,
396 = 2 × 2 × 3 × 3 × 11 = 2² × 3² × 11
✔ Prime factors:
2 × 2 × 3 × 3 × 11
---
🔢 7. 1260
- Divide by 2 → 1260 ÷ 2 = 630
- 630 ÷ 2 = 315
- 315 ÷ 3 = 105
- 105 ÷ 3 = 35
- 35 ÷ 5 = 7
- 7 is prime
- So,
1260 = 2 × 2 × 3 × 3 × 5 × 7 = 2² × 3² × 5 × 7
✔ Prime factors:
2 × 2 × 3 × 3 × 5 × 7
---
🔢 8. 686
- Divide by 2 → 686 ÷ 2 = 343
- 343 = 7 × 49 = 7 × 7 × 7 = 7³
- So,
686 = 2 × 7 × 7 × 7 = 2 × 7³
✔ Prime factors:
2 × 7 × 7 × 7
---
🔢 9. 3430
- Divide by 2 → 3430 ÷ 2 = 1715
- 1715 ÷ 5 = 343
- 343 = 7 × 7 × 7 = 7³
- So,
3430 = 2 × 5 × 7 × 7 × 7 = 2 × 5 × 7³
✔ Prime factors:
2 × 5 × 7 × 7 × 7
---
##
✔ Final Answers:
| Number | Prime Factorization |
|--------|---------------------|
| 55 | 5 × 11 |
| 105 | 3 × 5 × 7 |
| 260 | 2 × 2 × 5 × 13 |
| 390 | 2 × 3 × 5 × 13 |
| 882 | 2 × 3 × 3 × 7 × 7 |
| 396 | 2 × 2 × 3 × 3 × 11 |
| 1260 | 2 × 2 × 3 × 3 × 5 × 7 |
| 686 | 2 × 7 × 7 × 7 |
| 3430 | 2 × 5 × 7 × 7 × 7 |
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📝 How to Fill in the Worksheet:
For each box, write the
prime factorization step-by-step in the grid, and then write the final answer at the bottom (e.g., "5 × 11").
You can use the
factor tree method or
division method for clarity.
Let me know if you'd like a printable version with answers filled in!
Parent Tip: Review the logic above to help your child master the concept of prime factorization worksheet grade 5.
