Prime Factorization Worksheets - Math Monks - Free Printable

To solve the problem, we need to find the prime factors of each given number and construct the factor tree accordingly. Let's go through each number step by step.

---

1) 27

- Start with 27.
- Find two factors of 27: \( 27 = 3 \times 9 \).
- Now, factor 9: \( 9 = 3 \times 3 \).
- All factors are now prime.

Factor Tree:
```
27
/ \
3 9
/ \
3 3
```

Prime Factors: \( 3, 3, 3 \)

---

2) 30

- Start with 30.
- Find two factors of 30: \( 30 = 2 \times 15 \).
- Now, factor 15: \( 15 = 3 \times 5 \).
- All factors are now prime.

Factor Tree:
```
30
/ \
2 15
/ \
3 5
```

Prime Factors: \( 2, 3, 5 \)

---

3) 12

- Start with 12.
- Find two factors of 12: \( 12 = 2 \times 6 \).
- Now, factor 6: \( 6 = 2 \times 3 \).
- All factors are now prime.

Factor Tree:
```
12
/ \
2 6
/ \
2 3
```

Prime Factors: \( 2, 2, 3 \)

---

4) 28

- Start with 28.
- Find two factors of 28: \( 28 = 2 \times 14 \).
- Now, factor 14: \( 14 = 2 \times 7 \).
- All factors are now prime.

Factor Tree:
```
28
/ \
2 14
/ \
2 7
```

Prime Factors: \( 2, 2, 7 \)

---

5) 56

- Start with 56.
- Find two factors of 56: \( 56 = 2 \times 28 \).
- Now, factor 28: \( 28 = 2 \times 14 \).
- Next, factor 14: \( 14 = 2 \times 7 \).
- All factors are now prime.

Factor Tree:
```
56
/ \
2 28
/ \
2 14
/ \
2 7
```

Prime Factors: \( 2, 2, 2, 7 \)

---

6) 81

- Start with 81.
- Find two factors of 81: \( 81 = 3 \times 27 \).
- Now, factor 27: \( 27 = 3 \times 9 \).
- Next, factor 9: \( 9 = 3 \times 3 \).
- All factors are now prime.

Factor Tree:
```
81
/ \
3 27
/ \
3 9
/ \
3 3
```

Prime Factors: \( 3, 3, 3, 3 \)

---

Final Answers:

1. \( 27 \): \( 3, 3, 3 \)
2. \( 30 \): \( 2, 3, 5 \)
3. \( 12 \): \( 2, 2, 3 \)
4. \( 28 \): \( 2, 2, 7 \)
5. \( 56 \): \( 2, 2, 2, 7 \)
6. \( 81 \): \( 3, 3, 3, 3 \)

\boxed{
\begin{array}{ll}
1) & 3, 3, 3 \\
2) & 2, 3, 5 \\
3) & 2, 2, 3 \\
4) & 2, 2, 7 \\
5) & 2, 2, 2, 7 \\
6) & 3, 3, 3, 3 \\
\end{array}
}