Factor Tree Worksheets page - Free Printable

To solve the problems in the "Factor Tree Worksheet," we need to break down each number into its prime factors. A factor tree is a method used to find the prime factors of a given number by repeatedly dividing it by its factors until only prime numbers remain.

Let's solve each problem step by step:

---

Problem 1:

```
26
/ \
2 ?
```

- Start with 26.
- Divide 26 by 2 (since 2 is a factor): \( 26 \div 2 = 13 \).
- Check if 13 is a prime number: Yes, 13 is a prime number.
- The factor tree is complete.

Answer:
```
26
/ \
2 13
```

---

Problem 2:

```
42
/ \
? ?
```

- Start with 42.
- Divide 42 by 2 (since 2 is a factor): \( 42 \div 2 = 21 \).
- Now, factor 21:
- Divide 21 by 3 (since 3 is a factor): \( 21 \div 3 = 7 \).
- Check if 7 is a prime number: Yes, 7 is a prime number.
- The factor tree is complete.

Answer:
```
42
/ \
2 21
/ \
3 7
```

---

Problem 3:

```
55
/ \
? ?
```

- Start with 55.
- Divide 55 by 5 (since 5 is a factor): \( 55 \div 5 = 11 \).
- Check if 11 is a prime number: Yes, 11 is a prime number.
- The factor tree is complete.

Answer:
```
55
/ \
5 11
```

---

Problem 4:

```
42
/ \
? ?
```

- This is the same as Problem 2.
- Factorization: \( 42 = 2 \times 21 \), and \( 21 = 3 \times 7 \).

Answer:
```
42
/ \
2 21
/ \
3 7
```

---

Problem 5:

```
70
/ \
? ?
```

- Start with 70.
- Divide 70 by 2 (since 2 is a factor): \( 70 \div 2 = 35 \).
- Now, factor 35:
- Divide 35 by 5 (since 5 is a factor): \( 35 \div 5 = 7 \).
- Check if 7 is a prime number: Yes, 7 is a prime number.
- The factor tree is complete.

Answer:
```
70
/ \
2 35
/ \
5 7
```

---

Problem 6:

```
55
/ \
? ?
```

- This is the same as Problem 3.
- Factorization: \( 55 = 5 \times 11 \).

Answer:
```
55
/ \
5 11
```

---

Problem 7:

```
50
/ \
? ?
```

- Start with 50.
- Divide 50 by 2 (since 2 is a factor): \( 50 \div 2 = 25 \).
- Now, factor 25:
- Divide 25 by 5 (since 5 is a factor): \( 25 \div 5 = 5 \).
- Check if 5 is a prime number: Yes, 5 is a prime number.
- The factor tree is complete.

Answer:
```
50
/ \
2 25
/ \
5 5
```

---

Problem 8:

```
75
/ \
? ?
```

- Start with 75.
- Divide 75 by 3 (since 3 is a factor): \( 75 \div 3 = 25 \).
- Now, factor 25:
- Divide 25 by 5 (since 5 is a factor): \( 25 \div 5 = 5 \).
- Check if 5 is a prime number: Yes, 5 is a prime number.
- The factor tree is complete.

Answer:
```
75
/ \
3 25
/ \
5 5
```

---

Problem 9:

```
63
/ \
? ?
```

- Start with 63.
- Divide 63 by 3 (since 3 is a factor): \( 63 \div 3 = 21 \).
- Now, factor 21:
- Divide 21 by 3 (since 3 is a factor): \( 21 \div 3 = 7 \).
- Check if 7 is a prime number: Yes, 7 is a prime number.
- The factor tree is complete.

Answer:
```
63
/ \
3 21
/ \
3 7
```

---

Final Answers:

1. \( 26 = 2 \times 13 \)
2. \( 42 = 2 \times 3 \times 7 \)
3. \( 55 = 5 \times 11 \)
4. \( 42 = 2 \times 3 \times 7 \)
5. \( 70 = 2 \times 5 \times 7 \)
6. \( 55 = 5 \times 11 \)
7. \( 50 = 2 \times 5 \times 5 \)
8. \( 75 = 3 \times 5 \times 5 \)
9. \( 63 = 3 \times 3 \times 7 \)

\boxed{
\begin{array}{l}
1. 26 = 2 \times 13 \\
2. 42 = 2 \times 3 \times 7 \\
3. 55 = 5 \times 11 \\
4. 42 = 2 \times 3 \times 7 \\
5. 70 = 2 \times 5 \times 7 \\
6. 55 = 5 \times 11 \\
7. 50 = 2 \times 5 \times 5 \\
8. 75 = 3 \times 5 \times 5 \\
9. 63 = 3 \times 3 \times 7 \\
\end{array}
}