Prime Factorization Worksheet page - Free Printable

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

---

Problem 1:

Factor Tree for 32

```
32
/ \
4 8
/ \ / \
2 2 2 4
/ \
2 2
```

- Start with 32.
- Break it into 4 and 8.
- Break 4 into 2 and 2.
- Break 8 into 2 and 4.
- Break 4 into 2 and 2.
- The prime factors are: \(2, 2, 2, 2, 2\).

So, the final answer is:
\[ 32 = 2 \times 2 \times 2 \times 2 \times 2 \]

---

Problem 2:

Factor Tree for 50

```
50
/ \
5 10
/ \
2 5
```

- Start with 50.
- Break it into 5 and 10.
- Break 10 into 2 and 5.
- The prime factors are: \(2, 5, 5\).

So, the final answer is:
\[ 50 = 2 \times 5 \times 5 \]

---

Problem 3:

Factor Tree for 27

```
27
/ \
3 9
/ \
3 3
```

- Start with 27.
- Break it into 3 and 9.
- Break 9 into 3 and 3.
- The prime factors are: \(3, 3, 3\).

So, the final answer is:
\[ 27 = 3 \times 3 \times 3 \]

---

Problem 4:

Factor Tree for 10

```
10
/ \
2 5
```

- Start with 10.
- Break it into 2 and 5.
- Both 2 and 5 are prime numbers.

So, the final answer is:
\[ 10 = 2 \times 5 \]

---

Problem 5:

Factor Tree for 28

```
28
/ \
4 7
/ \
2 2
```

- Start with 28.
- Break it into 4 and 7.
- Break 4 into 2 and 2.
- The prime factors are: \(2, 2, 7\).

So, the final answer is:
\[ 28 = 2 \times 2 \times 7 \]

---

Problem 6:

Factor Tree for 48

```
48
/ \
6 8
/ \ / \
2 3 2 4
/ \
2 2
```

- Start with 48.
- Break it into 6 and 8.
- Break 6 into 2 and 3.
- Break 8 into 2 and 4.
- Break 4 into 2 and 2.
- The prime factors are: \(2, 2, 2, 2, 3\).

So, the final answer is:
\[ 48 = 2 \times 2 \times 2 \times 2 \times 3 \]

---

Final Answers:

1. \(32 = 2 \times 2 \times 2 \times 2 \times 2\)
2. \(50 = 2 \times 5 \times 5\)
3. \(27 = 3 \times 3 \times 3\)
4. \(10 = 2 \times 5\)
5. \(28 = 2 \times 2 \times 7\)
6. \(48 = 2 \times 2 \times 2 \times 2 \times 3\)

\[
\boxed{
\begin{array}{l}
1. 32 = 2 \times 2 \times 2 \times 2 \times 2 \\
2. 50 = 2 \times 5 \times 5 \\
3. 27 = 3 \times 3 \times 3 \\
4. 10 = 2 \times 5 \\
5. 28 = 2 \times 2 \times 7 \\
6. 48 = 2 \times 2 \times 2 \times 2 \times 3 \\
\end{array}
}
\]