Prime factor tree worksheet - Free Printable

Let's solve each problem step by step to find the prime factors of the given numbers using factor trees.

We'll break down each number into its prime factors, then fill in the factor tree and write the prime factorization.

---

1) 66

Start with 66.
Find two factors:
66 = 2 × 33
Now break down 33:
33 = 3 × 11

All are prime now.

So:
- 66 → 2 and 33
- 33 → 3 and 11

Prime Factors: 2 × 3 × 11 = 66

✔ Factor Tree:
```
66
/ \
2 33
/ \
3 11
```

---

2) 42

42 = 2 × 21
21 = 3 × 7

All are prime.

Prime Factors: 2 × 3 × 7 = 42

✔ Factor Tree:
```
42
/ \
2 21
/ \
3 7
```

---

3) 63

63 = 3 × 21
21 = 3 × 7

Prime Factors: 3 × 3 × 7 = 63
Or written as: 3² × 7

✔ Factor Tree:
```
63
/ \
3 21
/ \
3 7
```

---

4) 68

68 = 2 × 34
34 = 2 × 17

Prime Factors: 2 × 2 × 17 = 68
Or: 2² × 17

✔ Factor Tree:
```
68
/ \
2 34
/ \
2 17
```

---

5) 92

92 = 2 × 46
46 = 2 × 23

Prime Factors: 2 × 2 × 23 = 92
Or: 2² × 23

✔ Factor Tree:
```
92
/ \
2 46
/ \
2 23
```

---

6) 40

40 = 2 × 20
20 = 2 × 10
10 = 2 × 5

So:
- 40 → 2 and 20
- 20 → 2 and 10
- 10 → 2 and 5

Prime Factors: 2 × 2 × 2 × 5 = 40
Or: 2³ × 5

✔ Factor Tree:
```
40
/ \
2 20
/ \
2 10
/ \
2 5
```

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✔ Final Answers:

#### 1) 66
- Factor Tree:
- Top: 66
- Branches: 2 and 33
- 33 branches: 3 and 11
- Prime Factors: 2 × 3 × 11 = 66

#### 2) 42
- Factor Tree:
- 42 → 2 and 21
- 21 → 3 and 7
- Prime Factors: 2 × 3 × 7 = 42

#### 3) 63
- Factor Tree:
- 63 → 3 and 21
- 21 → 3 and 7
- Prime Factors: 3 × 3 × 7 = 63

#### 4) 68
- Factor Tree:
- 68 → 2 and 34
- 34 → 2 and 17
- Prime Factors: 2 × 2 × 17 = 68

#### 5) 92
- Factor Tree:
- 92 → 2 and 46
- 46 → 2 and 23
- Prime Factors: 2 × 2 × 23 = 92

#### 6) 40
- Factor Tree:
- 40 → 2 and 20
- 20 → 2 and 10
- 10 → 2 and 5
- Prime Factors: 2 × 2 × 2 × 5 = 40

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🔍 Summary Table:

| Number | Prime Factorization |
|--------|---------------------|
| 66 | 2 × 3 × 11 |
| 42 | 2 × 3 × 7 |
| 63 | 3 × 3 × 7 |
| 68 | 2 × 2 × 17 |
| 92 | 2 × 2 × 23 |
| 40 | 2 × 2 × 2 × 5 |

You can now fill in the circles and boxes in the worksheet accordingly!

Let me know if you'd like a printable version or visual diagrams!