Prime factor tree worksheet for practicing prime factorization with numbers 15, 14, 33, 12, 30, 27, 20, 28, and 45.

Let's solve each factor tree step by step and fill in the missing numbers. The goal is to break down each number into its prime factors using a factor tree, with prime numbers placed in the circles. Then, write the prime factorization as a product.

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1) 15

- 15 = 3 × 5 (both prime)
- So:
- Left circle: 3
- Right circle: 5
- Prime factorization:
15 = 3 × 5

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2) 14

- 14 = 2 × 7 (both prime)
- So:
- Left circle: 2
- Right circle: 7
- Prime factorization:
14 = 2 × 7

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3) 33

- 33 = 3 × 11 (both prime)
- So:
- Left circle: 3
- Right circle: 11
- Prime factorization:
33 = 3 × 11

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4) 12

Given:
- 12 splits into 6 and another number.
- Since 12 = 2 × 6 → so left circle = 2
- Now, 6 = 2 × 3
- So:
- Bottom left of 6: 2
- Bottom right of 6: 3
- Prime factorization:
12 = 2 × 2 × 3 or 2² × 3

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5) 30

Given:
- 30 splits into ? and 15
- 30 = 2 × 15 → so left circle = 2
- 15 = 3 × 5 → both prime
- So:
- Bottom left of 15: 3
- Bottom right of 15: 5
- Prime factorization:
30 = 2 × 3 × 5

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6) 27

Given:
- 27 splits into ? and 9
- 27 = 3 × 9 → so left circle = 3
- 9 = 3 × 3 → both prime
- So:
- Bottom left of 9: 3
- Bottom right of 9: 3
- Prime factorization:
27 = 3 × 3 × 3 or 3³

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7) 20

Given:
- 20 splits into ? and ?
- Let’s split 20 = 2 × 10 → so one circle = 2, other = 10
- Now, 10 = 2 × 5
- So:
- Bottom left of 10: 2
- Bottom right of 10: 5
- Prime factorization:
20 = 2 × 2 × 5 or 2² × 5

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8) 28

Given:
- 28 splits into ? and ?
- 28 = 2 × 14 → so one circle = 2, other = 14
- 14 = 2 × 7
- So:
- Bottom left of 14: 2
- Bottom right of 14: 7
- Prime factorization:
28 = 2 × 2 × 7 or 2² × 7

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9) 45

Given:
- 45 splits into ? and ?
- 45 = 5 × 9 → so one circle = 5, other = 9
- 9 = 3 × 3
- So:
- Bottom left of 9: 3
- Bottom right of 9: 3
- Prime factorization:
45 = 5 × 3 × 3 or 3² × 5

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✔ Final Answers:

| Problem | Factor Tree | Prime Factorization |
|--------|-------------|---------------------|
| 1) 15 | 3, 5 | 15 = 3 × 5 |
| 2) 14 | 2, 7 | 14 = 2 × 7 |
| 3) 33 | 3, 11 | 33 = 3 × 11 |
| 4) 12 | 2, then 2 and 3 | 12 = 2 × 2 × 3 |
| 5) 30 | 2, then 3 and 5 | 30 = 2 × 3 × 5 |
| 6) 27 | 3, then 3 and 3 | 27 = 3 × 3 × 3 |
| 7) 20 | 2, then 2 and 5 | 20 = 2 × 2 × 5 |
| 8) 28 | 2, then 2 and 7 | 28 = 2 × 2 × 7 |
| 9) 45 | 5, then 3 and 3 | 45 = 3 × 3 × 5 |

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🔍 Explanation Summary:

- A factor tree breaks a number down into two factors at each step until only prime numbers remain.
- Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves (e.g., 2, 3, 5, 7, 11, etc.).
- We always stop when all the branches end in primes.
- The final answer is the product of all the prime numbers in the circles.

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