Factor tree worksheet for practicing prime factorization of numbers.

To solve the problem of creating a factor tree for each number, we need to break down each number into its prime factors. A factor tree is a diagram that shows the breakdown of a number into its prime factors. Here's how we can approach each number:

---

1. Factor Tree for 40

- Start with 40.
- Break it down into two factors: \( 40 = 4 \times 10 \).
- Further break down 4 and 10:
- \( 4 = 2 \times 2 \)
- \( 10 = 2 \times 5 \)
- The prime factors are \( 2, 2, 2, \) and \( 5 \).

Factor Tree:
```
40
/ \
4 10
/ \ / \
2 2 2 5
```

---

2. Factor Tree for 54

- Start with 54.
- Break it down into two factors: \( 54 = 6 \times 9 \).
- Further break down 6 and 9:
- \( 6 = 2 \times 3 \)
- \( 9 = 3 \times 3 \)
- The prime factors are \( 2, 3, 3, \) and \( 3 \).

Factor Tree:
```
54
/ \
6 9
/ \ / \
2 3 3 3
```

---

3. Factor Tree for 25

- Start with 25.
- Break it down into two factors: \( 25 = 5 \times 5 \).
- Both factors are already prime.

Factor Tree:
```
25
/ \
5 5
```

---

4. Factor Tree for 21

- Start with 21.
- Break it down into two factors: \( 21 = 3 \times 7 \).
- Both factors are already prime.

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

---

5. Factor Tree for 13

- Start with 13.
- 13 is a prime number, so it cannot be broken down further.

Factor Tree:
```
13
```

---

6. Factor Tree for 30

- Start with 30.
- Break it down into two factors: \( 30 = 5 \times 6 \).
- Further break down 6:
- \( 6 = 2 \times 3 \)
- The prime factors are \( 2, 3, \) and \( 5 \).

Factor Tree:
```
30
/ \
5 6
/ \
2 3
```

---

7. Factor Tree for 42

- Start with 42.
- Break it down into two factors: \( 42 = 6 \times 7 \).
- Further break down 6:
- \( 6 = 2 \times 3 \)
- The prime factors are \( 2, 3, \) and \( 7 \).

Factor Tree:
```
42
/ \
6 7
/ \
2 3
```

---

8. Factor Tree for 18

- Start with 18.
- Break it down into two factors: \( 18 = 6 \times 3 \).
- Further break down 6:
- \( 6 = 2 \times 3 \)
- The prime factors are \( 2, 3, \) and \( 3 \).

Factor Tree:
```
18
/ \
6 3
/ \
2 3
```

---

Final Answer:

Here are the factor trees for all the numbers:

1. 40:
```
40
/ \
4 10
/ \ / \
2 2 2 5
```

2. 54:
```
54
/ \
6 9
/ \ / \
2 3 3 3
```

3. 25:
```
25
/ \
5 5
```

4. 21:
```
21
/ \
3 7
```

5. 13:
```
13
```

6. 30:
```
30
/ \
5 6
/ \
2 3
```

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

8. 18:
```
18
/ \
6 3
/ \
2 3
```

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{40} \\
\begin{array}{c}
40 \\
/ \ \ \\
4 10 \\
/ \ / \ \\
2 2 2 5 \\
\end{array} \\
2. \text{54} \\
\begin{array}{c}
54 \\
/ \ \ \\
6 9 \\
/ \ / \ \\
2 3 3 3 \\
\end{array} \\
3. \text{25} \\
\begin{array}{c}
25 \\
/ \ \ \\
5 5 \\
\end{array} \\
4. \text{21} \\
\begin{array}{c}
21 \\
/ \ \ \\
3 7 \\
\end{array} \\
5. \text{13} \\
\begin{array}{c}
13 \\
\end{array} \\
6. \text{30} \\
\begin{array}{c}
30 \\
/ \ \ \\
5 6 \\
/ \ \\
2 3 \\
\end{array} \\
7. \text{42} \\
\begin{array}{c}
42 \\
/ \ \ \\
6 7 \\
/ \ \\
2 3 \\
\end{array} \\
8. \text{18} \\
\begin{array}{c}
18 \\
/ \ \ \\
6 3 \\
/ \ \\
2 3 \\
\end{array}
\end{array}
}
\]