Students can practice breaking down composite numbers into their prime factors by completing these six factor tree exercises.

To solve the prime factorization problems, we need to break down each number into its prime factors using a factor tree. Let's go through each problem step by step.

---

Problem 1: 40

The factor tree is already provided:
```
40
/ \
2 20
/ \
2 10
/ \
2 5
```
- Start with 40.
- Split 40 into 2 and 20.
- Split 20 into 2 and 10.
- Split 10 into 2 and 5.
- All the numbers at the bottom are prime (2, 2, 2, 5).

So, the prime factorization of 40 is:
$$
40 = 2 \times 2 \times 2 \times 5
$$

---

Problem 2: 30

The factor tree is partially filled:
```
30
/ \
2 15
/ \
3 5
```
- Start with 30.
- Split 30 into 2 and 15.
- Split 15 into 3 and 5.
- All the numbers at the bottom are prime (2, 3, 5).

So, the prime factorization of 30 is:
$$
30 = 2 \times 3 \times 5
$$

---

Problem 3: 24

The factor tree is partially filled:
```
24
/ \
2 12
/ \
2 6
/ \
2 3
```
- Start with 24.
- Split 24 into 2 and 12.
- Split 12 into 2 and 6.
- Split 6 into 2 and 3.
- All the numbers at the bottom are prime (2, 2, 2, 3).

So, the prime factorization of 24 is:
$$
24 = 2 \times 2 \times 2 \times 3
$$

---

Problem 4: 18

The factor tree is partially filled:
```
18
/ \
2 9
/ \
3 3
```
- Start with 18.
- Split 18 into 2 and 9.
- Split 9 into 3 and 3.
- All the numbers at the bottom are prime (2, 3, 3).

So, the prime factorization of 18 is:
$$
18 = 2 \times 3 \times 3
$$

---

Problem 5: 36

The factor tree is partially filled:
```
36
/ \
2 18
/ \
2 9
/ \
3 3
```
- Start with 36.
- Split 36 into 2 and 18.
- Split 18 into 2 and 9.
- Split 9 into 3 and 3.
- All the numbers at the bottom are prime (2, 2, 3, 3).

So, the prime factorization of 36 is:
$$
36 = 2 \times 2 \times 3 \times 3
$$

---

Problem 6: 50

The factor tree is partially filled:
```
50
/ \
2 25
/ \
5 5
```
- Start with 50.
- Split 50 into 2 and 25.
- Split 25 into 5 and 5.
- All the numbers at the bottom are prime (2, 5, 5).

So, the prime factorization of 50 is:
$$
50 = 2 \times 5 \times 5
$$

---

Final Answers:

1. \( 40 = 2 \times 2 \times 2 \times 5 \)
2. \( 30 = 2 \times 3 \times 5 \)
3. \( 24 = 2 \times 2 \times 2 \times 3 \)
4. \( 18 = 2 \times 3 \times 3 \)
5. \( 36 = 2 \times 2 \times 3 \times 3 \)
6. \( 50 = 2 \times 5 \times 5 \)

$$
\boxed{
\begin{aligned}
1. & \ 2 \times 2 \times 2 \times 5 \\
2. & \ 2 \times 3 \times 5 \\
3. & \ 2 \times 2 \times 2 \times 3 \\
4. & \ 2 \times 3 \times 3 \\
5. & \ 2 \times 2 \times 3 \times 3 \\
6. & \ 2 \times 5 \times 5
\end{aligned}
}
$$