Factor tree worksheet for practicing prime factorization of numbers.

Let's solve each factor tree step by step. A factor tree breaks down a number into its prime factors by repeatedly dividing it into smaller factors until all the factors are prime numbers.

We’ll go through each number and complete the factor tree accordingly.

---

1. 42

Start with 42:
- 42 = 6 × 7 → 6 is not prime, so break it down
- 6 = 2 × 3 (both prime)

So:
```
42
/ \
6 7
/ \
2 3
```

✔ Prime factors: 2, 3, 7

---

2. 36

- 36 = 6 × 6
- 6 = 2 × 3

So:
```
36
/ \
6 6
/ \ / \
2 3 2 3
```

✔ Prime factors: 2, 2, 3, 3

---

3. 210

- 210 = 10 × 21
- 10 = 2 × 5
- 21 = 3 × 7

So:
```
210
/ \
10 21
/ \ / \
2 5 3 7
```

✔ Prime factors: 2, 3, 5, 7

---

4. 50

- 50 = 10 × 5
- 10 = 2 × 5

So:
```
50
/ \
10 5
/ \
2 5
```

✔ Prime factors: 2, 5, 5

---

5. 63

- 63 = 9 × 7
- 9 = 3 × 3

So:
```
63
/ \
9 7
/ \
3 3
```

✔ Prime factors: 3, 3, 7

---

6. 26

- 26 = 2 × 13 (both prime)

So:
```
26
/ \
2 13
```

✔ Prime factors: 2, 13

---

7. 42 (again)

Same as #1:

```
42
/ \
6 7
/ \
2 3
```

✔ Prime factors: 2, 3, 7

---

8. 45

- 45 = 9 × 5
- 9 = 3 × 3

So:
```
45
/ \
9 5
/ \
3 3
```

✔ Prime factors: 3, 3, 5

---

9. 85

- 85 = 5 × 17 (both prime)

So:
```
85
/ \
5 17
```

✔ Prime factors: 5, 17

---

10. 84

- 84 = 12 × 7
- 12 = 3 × 4 → 4 = 2 × 2

Alternatively: 84 = 2 × 42 → 42 = 2 × 21 → 21 = 3 × 7

So:
```
84
/ \
2 42
/ \
2 21
/ \
3 7
```

Or in the diagram format (two branches from 84):
```
84
/ \
12 7
/ \
2 6
/ \
2 3
```

But to match the structure (two branches from 84), let’s use:
- 84 = 2 × 42
- 42 = 6 × 7 → 6 = 2 × 3

So:
```
84
/ \
2 42
/ \
6 7
/ \
2 3
```

✔ Prime factors: 2, 2, 3, 7

---

11. 90

- 90 = 9 × 10
- 9 = 3 × 3
- 10 = 2 × 5

So:
```
90
/ \
9 10
/ \ / \
3 3 2 5
```

✔ Prime factors: 2, 3, 3, 5

---

12. 150

- 150 = 15 × 10
- 15 = 3 × 5
- 10 = 2 × 5

So:
```
150
/ \
15 10
/ \ / \
3 5 2 5
```

✔ Prime factors: 2, 3, 5, 5

---

✔ Final Answers (Filling in the blanks):

Here’s how you would fill each factor tree:

#### ① 42
```
42
/ \
6 7
/ \
2 3
```

#### ② 36
```
36
/ \
6 6
/ \ / \
2 3 2 3
```

#### ③ 210
```
210
/ \
10 21
/ \ / \
2 5 3 7
```

#### ④ 50
```
50
/ \
10 5
/ \
2 5
```

#### ⑤ 63
```
63
/ \
9 7
/ \
3 3
```

#### ⑥ 26
```
26
/ \
2 13
```

#### ⑦ 42 (same as ①)
```
42
/ \
6 7
/ \
2 3
```

#### ⑧ 45
```
45
/ \
9 5
/ \
3 3
```

#### ⑨ 85
```
85
/ \
5 17
```

#### ⑩ 84
```
84
/ \
2 42
/ \
6 7
/ \
2 3
```

#### ⑪ 90
```
90
/ \
9 10
/ \ / \
3 3 2 5
```

#### ⑫ 150
```
150
/ \
15 10
/ \ / \
3 5 2 5
```

---

📝 Summary of Prime Factorizations:

| Number | Prime Factors |
|--------|----------------|
| 42 | 2 × 3 × 7 |
| 36 | 2² × 3² |
| 210 | 2 × 3 × 5 × 7 |
| 50 | 2 × 5² |
| 63 | 3² × 7 |
| 26 | 2 × 13 |
| 42 | 2 × 3 × 7 |
| 45 | 3² × 5 |
| 85 | 5 × 17 |
| 84 | 2² × 3 × 7 |
| 90 | 2 × 3² × 5 |
| 150 | 2 × 3 × 5² |

You can now fill in the blanks on your worksheet using these trees!

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