Let’s solve each number step by step using factor trees. We’ll break each number down into its prime factors, then write the answer in index notation (like 2⁴).
---
1. 36
Start with 36.
- 36 = 2 × 18 → 2 is prime (blue circle), 18 is not (yellow box)
- 18 = 2 × 9 → 2 is prime, 9 is not
- 9 = 3 × 3 → both are prime
So:
36 = 2 × 2 × 3 × 3
In index notation:
2² × 3²
---
2. 54
Start with 54.
- 54 = 2 × 27 → 2 is prime, 27 is not
- 27 = 3 × 9 → 3 is prime, 9 is not
- 9 = 3 × 3 → both prime
So:
54 = 2 × 3 × 3 × 3
In index notation:
2 × 3³
---
3. 135
Start with 135.
- 135 = 3 × 45 → 3 is prime, 45 is not
- 45 = 3 × 15 → 3 is prime, 15 is not
- 15 = 3 × 5 → both prime
So:
135 = 3 × 3 × 3 × 5
In index notation:
3³ × 5
---
4. 525
Start with 525.
- 525 = 3 × 175 → 3 is prime, 175 is not
- 175 = 5 × 35 → 5 is prime, 35 is not
- 35 = 5 × 7 → both prime
So:
525 = 3 × 5 × 5 × 7
In index notation:
3 × 5² × 7
---
5. 693
Start with 693.
- 693 = 3 × 231 → 3 is prime, 231 is not
- 231 = 3 × 77 → 3 is prime, 77 is not
- 77 = 7 × 11 → both prime
So:
693 = 3 × 3 × 7 × 11
In index notation:
3² × 7 × 11
---
Final Answer:
36 = 2² × 3²
54 = 2 × 3³
135 = 3³ × 5
525 = 3 × 5² × 7
693 = 3² × 7 × 11
Parent Tip: Review the logic above to help your child master the concept of factor tree worksheet.
