Sure! Let’s solve each problem step by step. The goal is to find the
prime factors of each number using a
factor tree, and then write them as a multiplication sentence.
---
🔢 1) Prime Factors of 20
Start with 20.
- 20 can be split into 2 × 10 (since 2 is prime, we keep it; 10 is not prime).
- Now factor 10 → 2 × 5 (both 2 and 5 are prime).
✔ So the prime factors are:
2 × 2 × 5
> You can write this as:
>
Prime Factors: 2 × 2 × 5 = 20
---
🔢 2) Prime Factors of 99
Start with 99.
- 99 = 9 × 11 (11 is prime; 9 is not).
- Factor 9 → 3 × 3 (both are prime).
✔ So the prime factors are:
3 × 3 × 11
> Write:
>
Prime Factors: 3 × 3 × 11 = 99
---
🔢 3) Prime Factors of 45
Start with 45.
- 45 = 5 × 9 (5 is prime; 9 is not).
- Factor 9 → 3 × 3 (both prime).
✔ So the prime factors are:
3 × 3 × 5
> Write:
>
Prime Factors: 3 × 3 × 5 = 45
---
🔢 4) Prime Factors of 28
Start with 28.
- 28 = 2 × 14 (2 is prime; 14 is not).
- Factor 14 → 2 × 7 (both prime).
✔ So the prime factors are:
2 × 2 × 7
> Write:
>
Prime Factors: 2 × 2 × 7 = 28
---
🔢 5) Prime Factors of 52
Start with 52.
- 52 = 2 × 26 (2 is prime; 26 is not).
- Factor 26 → 2 × 13 (both prime).
✔ So the prime factors are:
2 × 2 × 13
> Write:
>
Prime Factors: 2 × 2 × 13 = 52
---
🔢 6) Prime Factors of 30
Start with 30.
- 30 = 2 × 15 (2 is prime; 15 is not).
- Factor 15 → 3 × 5 (both prime).
✔ So the prime factors are:
2 × 3 × 5
> Write:
>
Prime Factors: 2 × 3 × 5 = 30
---
##
✔ Final Answers:
1)
2 × 2 × 5 = 20
2)
3 × 3 × 11 = 99
3)
3 × 3 × 5 = 45
4)
2 × 2 × 7 = 28
5)
2 × 2 × 13 = 52
6)
2 × 3 × 5 = 30
---
## 📝 Notes for the Factor Tree Diagrams:
For each tree:
- Top box: original number.
- First split: any two factors (one should ideally be prime if possible).
- Keep splitting non-prime numbers until all branches end in
prime numbers (circles at bottom).
- Multiply all primes at the bottom to check your answer.
Example for 20:
```
20
/ \
2 10
/ \
2 5
```
All leaves (bottom circles): 2, 2, 5 → correct!
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Let me know if you’d like to see the filled-in diagrams or need help drawing them!
Parent Tip: Review the logic above to help your child master the concept of multiple and factors worksheet.
