Prime Factor Tree Worksheets - Free Printable

To complete the prime factor trees for each numeral, we need to break down each number into its prime factors step by step. Let's solve each problem systematically.

---

1) Prime Factor Tree for 45

The given tree is:
```
45
/ \
? 3
/ \
3 ?
```

#### Steps:
1. Start with 45.
2. Divide 45 by the smallest prime number, which is 3:
\( 45 \div 3 = 15 \). So, the first split is \( 45 = 3 \times 15 \).
3. Now, factorize 15. Divide 15 by 3:
\( 15 \div 3 = 5 \). So, \( 15 = 3 \times 5 \).
4. The number 5 is already a prime number.

#### Final Tree:
```
45
/ \
15 3
/ \
3 5
```

---

2) Prime Factor Tree for 24

The given tree is:
```
24
/ \
4 ?
/ \
2 ?
\
2
```

#### Steps:
1. Start with 24.
2. Divide 24 by the smallest prime number, which is 2:
\( 24 \div 2 = 12 \). So, the first split is \( 24 = 2 \times 12 \).
3. Now, factorize 12. Divide 12 by 2:
\( 12 \div 2 = 6 \). So, \( 12 = 2 \times 6 \).
4. Next, factorize 6. Divide 6 by 2:
\( 6 \div 2 = 3 \). So, \( 6 = 2 \times 3 \).
5. The number 3 is already a prime number.

#### Final Tree:
```
24
/ \
4 6
/ \ / \
2 2 2 3
```

---

3) Prime Factor Tree for 32

The given tree is:
```
32
/ \
? 4
/ \
4 2
/ \
2 2
```

#### Steps:
1. Start with 32.
2. Divide 32 by the smallest prime number, which is 2:
\( 32 \div 2 = 16 \). So, the first split is \( 32 = 2 \times 16 \).
3. Now, factorize 16. Divide 16 by 2:
\( 16 \div 2 = 8 \). So, \( 16 = 2 \times 8 \).
4. Next, factorize 8. Divide 8 by 2:
\( 8 \div 2 = 4 \). So, \( 8 = 2 \times 4 \).
5. Finally, factorize 4. Divide 4 by 2:
\( 4 \div 2 = 2 \). So, \( 4 = 2 \times 2 \).

#### Final Tree:
```
32
/ \
2 16
/ \
2 8
/ \
2 4
/ \
2 2
```

---

4) Prime Factor Tree for 12

The given tree is:
```
12
/ \
? 6
/ \
2 ?
```

#### Steps:
1. Start with 12.
2. Divide 12 by the smallest prime number, which is 2:
\( 12 \div 2 = 6 \). So, the first split is \( 12 = 2 \times 6 \).
3. Now, factorize 6. Divide 6 by 2:
\( 6 \div 2 = 3 \). So, \( 6 = 2 \times 3 \).
4. The number 3 is already a prime number.

#### Final Tree:
```
12
/ \
2 6
/ \
2 3
```

---

5) Prime Factor Tree for 8

The given tree is:
```
8
/ \
2 ?
/ \
? 2
```

#### Steps:
1. Start with 8.
2. Divide 8 by the smallest prime number, which is 2:
\( 8 \div 2 = 4 \). So, the first split is \( 8 = 2 \times 4 \).
3. Now, factorize 4. Divide 4 by 2:
\( 4 \div 2 = 2 \). So, \( 4 = 2 \times 2 \).

#### Final Tree:
```
8
/ \
2 4
/ \
2 2
```

---

6) Prime Factor Tree for 42

The given tree is:
```
42
/ \
? 14
\
7
\
?
```

#### Steps:
1. Start with 42.
2. Divide 42 by the smallest prime number, which is 2:
\( 42 \div 2 = 21 \). So, the first split is \( 42 = 2 \times 21 \).
3. Now, factorize 21. Divide 21 by 3:
\( 21 \div 3 = 7 \). So, \( 21 = 3 \times 7 \).
4. The numbers 3 and 7 are already prime numbers.

#### Final Tree:
```
42
/ \
2 21
/ \
3 7
```

---

Final Answers:

1.
```
45
/ \
15 3
/ \
3 5
```
2.
```
24
/ \
4 6
/ \ / \
2 2 2 3
```
3.
```
32
/ \
2 16
/ \
2 8
/ \
2 4
/ \
2 2
```
4.
```
12
/ \
2 6
/ \
2 3
```
5.
```
8
/ \
2 4
/ \
2 2
```
6.
```
42
/ \
2 21
/ \
3 7
```

Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
1) \begin{array}{c}
45 \\
/ \backslash \\
15 3 \\
/ \backslash \\
3 5
\end{array} \\
2) \begin{array}{c}
24 \\
/ \backslash \\
4 6 \\
/ \backslash / \backslash \\
2 2 2 3
\end{array} \\
3) \begin{array}{c}
32 \\
/ \backslash \\
2 16 \\
/ \backslash \\
2 8 \\
/ \backslash \\
2 4 \\
/ \backslash \\
2 2
\end{array} \\
4) \begin{array}{c}
12 \\
/ \backslash \\
2 6 \\
/ \backslash \\
2 3
\end{array} \\
5) \begin{array}{c}
8 \\
/ \backslash \\
2 4 \\
/ \backslash \\
2 2
\end{array} \\
6) \begin{array}{c}
42 \\
/ \backslash \\
2 21 \\
/ \backslash \\
3 7
\end{array}
\end{array}
}
\]