Primes and Composites Worksheets | Printable PDF Worksheets - Free Printable

Let's solve each of the prime factor trees step by step and fill in the blanks. The goal is to break down each number into its prime factors using a factor tree.

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🔹 Key:

- Blue circles (○) = Prime factors
- Yellow rectangles (□) = Not prime (composite) factors

We'll go through each number:

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## ✔ 1. 32

Start with 32:
- 32 ÷ 2 = 16 → 2 is prime
- 16 ÷ 2 = 8 → 2 is prime
- 8 ÷ 2 = 4 → 2 is prime
- 4 ÷ 2 = 2 → 2 is prime
- 2 ÷ 2 = 1

So, all factors are 2s.

Factor Tree:
```
32
/ \
2 16
/ \
2 8
/ \
2 4
/ \
2 2
```

But since we need to fill in the boxes:

- Top: 32 → split into 2 (prime) and 16 (not prime)
- Then 16 → 2 (prime) and 8 (not prime)
- Then 8 → 2 (prime) and 4 (not prime)
- Then 4 → 2 (prime) and 2 (prime)

✔ So:
- 32 = 2 × 2 × 2 × 2 × 2 = 2⁵

> Answer: `32 = 2⁵` or `2 × 2 × 2 × 2 × 2`

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## ✔ 2. 108

Break down 108:

- 108 ÷ 2 = 54 → 2 is prime
- 54 ÷ 2 = 27 → 2 is prime
- 27 ÷ 3 = 9 → 3 is prime
- 9 ÷ 3 = 3 → 3 is prime
- 3 ÷ 3 = 1

So: 108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

Factor Tree:
```
108
/ \
2 54
/ \
2 27
/ \
3 9
/ \
3 3
```

Fill in:
- 108 → 2 (prime), 54 (not prime)
- 54 → 2 (prime), 27 (not prime)
- 27 → 3 (prime), 9 (not prime)
- 9 → 3 (prime), 3 (prime)

✔ So:
- 108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

> Answer: `108 = 2² × 3³`

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## ✔ 3. 450

Break down 450:

- 450 ÷ 2 = 225 → 2 is prime
- 225 ÷ 3 = 75 → 3 is prime
- 75 ÷ 3 = 25 → 3 is prime
- 25 ÷ 5 = 5 → 5 is prime
- 5 ÷ 5 = 1

So: 450 = 2 × 3 × 3 × 5 × 5 = 2 × 3² × 5²

Factor Tree:
```
450
/ \
2 225
/ \
3 75
/ \
3 25
/ \
5 5
```

Fill in:
- 450 → 2 (prime), 225 (not prime)
- 225 → 3 (prime), 75 (not prime)
- 75 → 3 (prime), 25 (not prime)
- 25 → 5 (prime), 5 (prime)

✔ So:
- 450 = 2 × 3² × 5²

> Answer: `450 = 2 × 3² × 5²`

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## ✔ 4. 1050

Break down 1050:

- 1050 ÷ 2 = 525 → 2 is prime
- 525 ÷ 3 = 175 → 3 is prime
- 175 ÷ 5 = 35 → 5 is prime
- 35 ÷ 5 = 7 → 5 is prime
- 7 ÷ 7 = 1 → 7 is prime

So: 1050 = 2 × 3 × 5 × 5 × 7 = 2 × 3 × 5² × 7

Factor Tree:
```
1050
/ \
2 525
/ \
3 175
/ \
5 35
/ \
5 7
```

Fill in:
- 1050 → 2 (prime), 525 (not prime)
- 525 → 3 (prime), 175 (not prime)
- 175 → 5 (prime), 35 (not prime)
- 35 → 5 (prime), 7 (prime)

✔ So:
- 1050 = 2 × 3 × 5² × 7

> Answer: `1050 = 2 × 3 × 5² × 7`

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## ✔ 5. 1323

Check if divisible by small primes:

- 1323 is odd → not divisible by 2
- Sum of digits: 1+3+2+3 = 9 → divisible by 3

So:
- 1323 ÷ 3 = 441 → 3 is prime
- 441 ÷ 3 = 147 → 3 is prime
- 147 ÷ 3 = 49 → 3 is prime
- 49 ÷ 7 = 7 → 7 is prime
- 7 ÷ 7 = 1

So: 1323 = 3 × 3 × 3 × 7 × 7 = 3³ × 7²

Factor Tree:
```
1323
/ \
3 441
/ \
3 147
/ \
3 49
/ \
7 7
```

Fill in:
- 1323 → 3 (prime), 441 (not prime)
- 441 → 3 (prime), 147 (not prime)
- 147 → 3 (prime), 49 (not prime)
- 49 → 7 (prime), 7 (prime)

✔ So:
- 1323 = 3³ × 7²

> Answer: `1323 = 3³ × 7²`

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## ✔ 6. 2925

Break down 2925:

- Ends in 5 → divisible by 5
- 2925 ÷ 5 = 585 → 5 is prime
- 585 ÷ 5 = 117 → 5 is prime
- 117 → sum of digits: 1+1+7=9 → divisible by 3
- 117 ÷ 3 = 39 → 3 is prime
- 39 ÷ 3 = 13 → 3 is prime
- 13 is prime

So: 2925 = 5 × 5 × 3 × 3 × 13 = 5² × 3² × 13

Factor Tree:
```
2925
/ \
5 585
/ \
5 117
/ \
3 39
/ \
3 13
```

Fill in:
- 2925 → 5 (prime), 585 (not prime)
- 585 → 5 (prime), 117 (not prime)
- 117 → 3 (prime), 39 (not prime)
- 39 → 3 (prime), 13 (prime)

✔ So:
- 2925 = 3² × 5² × 13

> Answer: `2925 = 3² × 5² × 13`

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✔ Final Answers:

| Number | Prime Factorization |
|--------|---------------------|
| 32 | 2⁵ |
| 108 | 2² × 3³ |
| 450 | 2 × 3² × 5² |
| 1050 | 2 × 3 × 5² × 7 |
| 1323 | 3³ × 7² |
| 2925 | 3² × 5² × 13 |

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📌 How to Fill in the Trees:

For each tree, follow this pattern:

- Top number splits into one prime (blue circle) and one non-prime (yellow rectangle)
- Continue breaking down non-prime numbers until all branches end in primes

You can now complete the worksheet accordingly.

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Let me know if you'd like a visual version of the completed trees!