Prime Factorization Worksheets - Math Monks - Free Printable

I'll solve each prime factorization problem step by step, working through the factor trees carefully.

Problem 1: 54
- 54 = 2 × 27 (2 is prime)
- 27 = 3 × 9 (3 is prime)
- 9 = 3 × 3 (both are prime)
- So: 54 = 2 × 3 × 3 × 3 = 2 × 3³

Problem 2: 88
- 88 = 2 × 44 (2 is prime)
- 44 = 2 × 22 (2 is prime)
- 22 = 2 × 11 (both are prime)
- So: 88 = 2 × 2 × 2 × 11 = 2³ × 11

Problem 3: 24
- 24 = 2 × 12 (2 is prime)
- 12 = 2 × 6 (2 is prime)
- 6 = 2 × 3 (both are prime)
- So: 24 = 2 × 2 × 2 × 3 = 2³ × 3

Problem 4: 102
- 102 = 2 × 51 (2 is prime)
- 51 = 3 × 17 (both are prime)
- So: 102 = 2 × 3 × 17

Problem 5: 175
- 175 = 5 × 35 (5 is prime)
- 35 = 5 × 7 (both are prime)
- So: 175 = 5 × 5 × 7 = 5² × 7

Problem 6: 160
- 160 = 2 × 80 (2 is prime)
- 80 = 2 × 40 (2 is prime)
- 40 = 2 × 20 (2 is prime)
- 20 = 2 × 10 (2 is prime)
- 10 = 2 × 5 (both are prime)
- So: 160 = 2 × 2 × 2 × 2 × 2 × 5 = 2⁵ × 5

Problem 7: 375
- 375 = 3 × 125 (3 is prime)
- 125 = 5 × 25 (5 is prime)
- 25 = 5 × 5 (both are prime)
- So: 375 = 3 × 5 × 5 × 5 = 3 × 5³

Problem 8: 625
- 625 = 5 × 125 (5 is prime)
- 125 = 5 × 25 (5 is prime)
- 25 = 5 × 5 (both are prime)
- So: 625 = 5 × 5 × 5 × 5 = 5⁴

Problem 9: 294
- 294 = 2 × 147 (2 is prime)
- 147 = 3 × 49 (3 is prime)
- 49 = 7 × 7 (both are prime)
- So: 294 = 2 × 3 × 7 × 7 = 2 × 3 × 7²

Let me verify my calculations:
- 54: 2 × 3³ = 2 × 27 = 54 ✓
- 88: 2³ × 11 = 8 × 11 = 88 ✓
- 24: 2³ × 3 = 8 × 3 = 24 ✓
- 102: 2 × 3 × 17 = 6 × 17 = 102 ✓
- 175: 5² × 7 = 25 × 7 = 175 ✓
- 160: 2⁵ × 5 = 32 × 5 = 160 ✓
- 375: 3 × 5³ = 3 × 125 = 375 ✓
- 625: 5⁴ = 625 ✓
- 294: 2 × 3 × 7² = 6 × 49 = 294 ✓

Final Answer:
1) 54 = 2 × 3³
2) 88 = 2³ × 11
3) 24 = 2³ × 3
4) 102 = 2 × 3 × 17
5) 175 = 5² × 7
6) 160 = 2⁵ × 5
7) 375 = 3 × 5³
8) 625 = 5⁴
9) 294 = 2 × 3 × 7²