Prime factorization worksheet with six problems using factor trees.

I'll work through each problem step by step to find the prime factors of each number.

Problem 1: Find prime factors of 20
- Start with 20
- Divide by smallest prime: 20 ÷ 2 = 10
- Continue: 10 ÷ 2 = 5
- 5 is prime, so we stop
- Prime factors: 2 × 2 × 5 = 20

Problem 2: Find prime factors of 99
- Start with 99
- Try dividing by 2: doesn't work (99 is odd)
- Try 3: 99 ÷ 3 = 33
- Continue: 33 ÷ 3 = 11
- 11 is prime, so we stop
- Prime factors: 3 × 3 × 11 = 99

Problem 3: Find prime factors of 45
- Start with 45
- Try dividing by 2: doesn't work (45 is odd)
- Try 3: 45 ÷ 3 = 15
- Continue: 15 ÷ 3 = 5
- 5 is prime, so we stop
- Prime factors: 3 × 3 × 5 = 45

Problem 4: Find prime factors of 28
- Start with 28
- Divide by 2: 28 ÷ 2 = 14
- Continue: 14 ÷ 2 = 7
- 7 is prime, so we stop
- Prime factors: 2 × 2 × 7 = 28

Problem 5: Find prime factors of 52
- Start with 52
- Divide by 2: 52 ÷ 2 = 26
- Continue: 26 ÷ 2 = 13
- 13 is prime, so we stop
- Prime factors: 2 × 2 × 13 = 52

Problem 6: Find prime factors of 30
- Start with 30
- Divide by 2: 30 ÷ 2 = 15
- Continue: 15 ÷ 3 = 5
- 5 is prime, so we stop
- Prime factors: 2 × 3 × 5 = 30

Let me verify my calculations:
1) 2 × 2 × 5 = 4 × 5 = 20 ✓
2) 3 × 3 × 11 = 9 × 11 = 99 ✓
3) 3 × 3 × 5 = 9 × 5 = 45 ✓
4) 2 × 2 × 7 = 4 × 7 = 28 ✓
5) 2 × 2 × 13 = 4 × 13 = 52 ✓
6) 2 × 3 × 5 = 6 × 5 = 30 ✓

All calculations are correct!

Final Answer:
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