Complete the prime factor tree for each number with this math worksheet.

To solve the problem of completing the prime factor trees for each number, we need to break down each given number into its prime factors. Let's go through each number step by step.

Problem: Complete the prime factor tree for each number.

#### Number 1: 30
1. Start with 30.
2. Find two factors of 30. For example, \(30 = 6 \times 5\).
3. Check if 6 is a prime number. Since it is not, break it down further: \(6 = 2 \times 3\).
4. Both 2 and 3 are prime numbers, and 5 is already a prime number.
5. The prime factorization of 30 is \(2 \times 3 \times 5\).

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

#### Number 2: 48
1. Start with 48.
2. Find two factors of 48. For example, \(48 = 6 \times 8\).
3. Check if 6 is a prime number. Since it is not, break it down further: \(6 = 2 \times 3\).
4. Check if 8 is a prime number. Since it is not, break it down further: \(8 = 2 \times 4\).
5. Check if 4 is a prime number. Since it is not, break it down further: \(4 = 2 \times 2\).
6. All the factors are now prime numbers.
7. The prime factorization of 48 is \(2 \times 2 \times 2 \times 2 \times 3\).

Prime Factor Tree:
```
48
/ \
6 8
/ \ / \
2 3 2 4
/ \
2 2
```

#### Number 3: 54
1. Start with 54.
2. Find two factors of 54. For example, \(54 = 6 \times 9\).
3. Check if 6 is a prime number. Since it is not, break it down further: \(6 = 2 \times 3\).
4. Check if 9 is a prime number. Since it is not, break it down further: \(9 = 3 \times 3\).
5. All the factors are now prime numbers.
6. The prime factorization of 54 is \(2 \times 3 \times 3 \times 3\).

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

#### Number 4: 72
1. Start with 72.
2. Find two factors of 72. For example, \(72 = 8 \times 9\).
3. Check if 8 is a prime number. Since it is not, break it down further: \(8 = 2 \times 4\).
4. Check if 4 is a prime number. Since it is not, break it down further: \(4 = 2 \times 2\).
5. Check if 9 is a prime number. Since it is not, break it down further: \(9 = 3 \times 3\).
6. All the factors are now prime numbers.
7. The prime factorization of 72 is \(2 \times 2 \times 2 \times 3 \times 3\).

Prime Factor Tree:
```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```

#### Number 5: 90
1. Start with 90.
2. Find two factors of 90. For example, \(90 = 10 \times 9\).
3. Check if 10 is a prime number. Since it is not, break it down further: \(10 = 2 \times 5\).
4. Check if 9 is a prime number. Since it is not, break it down further: \(9 = 3 \times 3\).
5. All the factors are now prime numbers.
6. The prime factorization of 90 is \(2 \times 3 \times 3 \times 5\).

Prime Factor Tree:
```
90
/ \
10 9
/ \ / \
2 5 3 3
```

#### Number 6: 108
1. Start with 108.
2. Find two factors of 108. For example, \(108 = 12 \times 9\).
3. Check if 12 is a prime number. Since it is not, break it down further: \(12 = 3 \times 4\).
4. Check if 4 is a prime number. Since it is not, break it down further: \(4 = 2 \times 2\).
5. Check if 9 is a prime number. Since it is not, break it down further: \(9 = 3 \times 3\).
6. All the factors are now prime numbers.
7. The prime factorization of 108 is \(2 \times 2 \times 3 \times 3 \times 3\).

Prime Factor Tree:
```
108
/ \
12 9
/ \ / \
3 4 3 3
/ \
2 2
```

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{30: } 2 \times 3 \times 5 \\
\text{48: } 2 \times 2 \times 2 \times 2 \times 3 \\
\text{54: } 2 \times 3 \times 3 \times 3 \\
\text{72: } 2 \times 2 \times 2 \times 3 \times 3 \\
\text{90: } 2 \times 3 \times 3 \times 5 \\
\text{108: } 2 \times 2 \times 3 \times 3 \times 3 \\
\end{array}
}
\]