Let me work through each factor tree problem step by step.
Problem 1: 15
- 15 can be broken down into: 3 × 5
- Both 3 and 5 are prime numbers
- Answer: 15 = 3 × 5
Problem 2: 14
- 14 can be broken down into: 2 × 7
- Both 2 and 7 are prime numbers
- Answer: 14 = 2 × 7
Problem 3: 33
- 33 can be broken down into: 3 × 11
- Both 3 and 11 are prime numbers
- Answer: 33 = 3 × 11
Problem 4: 12
- First split: 12 = 2 × 6 (2 is prime)
- Then split 6: 6 = 2 × 3 (both are prime)
- So: 12 = 2 × 2 × 3
Problem 5: 30
- First split: 30 = 2 × 15 (2 is prime)
- Then split 15: 15 = 3 × 5 (both are prime)
- So: 30 = 2 × 3 × 5
Problem 6: 27
- First split: 27 = 3 × 9 (3 is prime)
- Then split 9: 9 = 3 × 3 (both are prime)
- So: 27 = 3 × 3 × 3
Problem 7: 20
- First split: 20 = 2 × 10 (2 is prime)
- Then split 10: 10 = 2 × 5 (both are prime)
- So: 20 = 2 × 2 × 5
Problem 8: 28
- First split: 28 = 2 × 14 (2 is prime)
- Then split 14: 14 = 2 × 7 (both are prime)
- So: 28 = 2 × 2 × 7
Problem 9: 45
- First split: 45 = 3 × 15 (3 is prime) or 45 = 5 × 9
- Let's use 3 × 15, then split 15: 15 = 3 × 5
- So: 45 = 3 × 3 × 5
- Alternatively: 45 = 5 × 9, then 9 = 3 × 3, so 45 = 5 × 3 × 3 (same answer)
Let me verify my answers:
1. 3 × 5 = 15 ✓
2. 2 × 7 = 14 ✓
3. 3 × 11 = 33 ✓
4. 2 × 2 × 3 = 12 ✓
5. 2 × 3 × 5 = 30 ✓
6. 3 × 3 × 3 = 27 ✓
7. 2 × 2 × 5 = 20 ✓
8. 2 × 2 × 7 = 28 ✓
9. 3 × 3 × 5 = 45 ✓
All calculations check out!
Final Answer:
1) 15 = 3 × 5
2) 14 = 2 × 7
3) 33 = 3 × 11
4) 12 = 2 × 2 × 3
5) 30 = 2 × 3 × 5
6) 27 = 3 × 3 × 3
7) 20 = 2 × 2 × 5
8) 28 = 2 × 2 × 7
9) 45 = 3 × 3 × 5
Parent Tip: Review the logic above to help your child master the concept of lcm factor tree worksheet.
