Prime Factorization Practice Worksheet - Find the prime factors of numbers using tree diagrams.

Problem: Prime Factorization Practice

The task is to find the prime factors of the given numbers using a factor tree method. Here's how we can solve each problem step by step.

---

#### Step 1: Understand the Factor Tree Method
A factor tree breaks down a number into its prime factors. We start with the given number and repeatedly divide it by its smallest prime factor until all factors are prime.

#### Step 2: Solve Each Problem

---

##### Problem 1: 27
- Start with 27.
- Divide by the smallest prime factor, which is 3:
$$
27 \div 3 = 9
$$
- Now, factor 9:
$$
9 \div 3 = 3
$$
- Both 3 and 3 are prime numbers.
- The prime factorization of 27 is:
$$
27 = 3 \times 3 \times 3
$$

##### Problem 2: 20
- Start with 20.
- Divide by the smallest prime factor, which is 2:
$$
20 \div 2 = 10
$$
- Now, factor 10:
$$
10 \div 2 = 5
$$
- Both 2, 2, and 5 are prime numbers.
- The prime factorization of 20 is:
$$
20 = 2 \times 2 \times 5
$$

##### Problem 3: 63
- Start with 63.
- Divide by the smallest prime factor, which is 3:
$$
63 \div 3 = 21
$$
- Now, factor 21:
$$
21 \div 3 = 7
$$
- Both 3, 3, and 7 are prime numbers.
- The prime factorization of 63 is:
$$
63 = 3 \times 3 \times 7
$$

##### Problem 4: 325
- Start with 325.
- Divide by the smallest prime factor, which is 5:
$$
325 \div 5 = 65
$$
- Now, factor 65:
$$
65 \div 5 = 13
$$
- Both 5, 5, and 13 are prime numbers.
- The prime factorization of 325 is:
$$
325 = 5 \times 5 \times 13
$$

##### Problem 5: 52
- Start with 52.
- Divide by the smallest prime factor, which is 2:
$$
52 \div 2 = 26
$$
- Now, factor 26:
$$
26 \div 2 = 13
$$
- Both 2, 2, and 13 are prime numbers.
- The prime factorization of 52 is:
$$
52 = 2 \times 2 \times 13
$$

##### Problem 6: 68
- Start with 68.
- Divide by the smallest prime factor, which is 2:
$$
68 \div 2 = 34
$$
- Now, factor 34:
$$
34 \div 2 = 17
$$
- Both 2, 2, and 17 are prime numbers.
- The prime factorization of 68 is:
$$
68 = 2 \times 2 \times 17
$$

##### Problem 7: 45
- Start with 45.
- Divide by the smallest prime factor, which is 3:
$$
45 \div 3 = 15
$$
- Now, factor 15:
$$
15 \div 3 = 5
$$
- Both 3, 3, and 5 are prime numbers.
- The prime factorization of 45 is:
$$
45 = 3 \times 3 \times 5
$$

##### Problem 8: 92
- Start with 92.
- Divide by the smallest prime factor, which is 2:
$$
92 \div 2 = 46
$$
- Now, factor 46:
$$
46 \div 2 = 23
$$
- Both 2, 2, and 23 are prime numbers.
- The prime factorization of 92 is:
$$
92 = 2 \times 2 \times 23
$$

##### Problem 9: 114
- Start with 114.
- Divide by the smallest prime factor, which is 2:
$$
114 \div 2 = 57
$$
- Now, factor 57:
$$
57 \div 3 = 19
$$
- Both 2, 3, and 19 are prime numbers.
- The prime factorization of 114 is:
$$
114 = 2 \times 3 \times 19
$$

---

#### Final Answer
$$
\boxed{
\begin{aligned}
&27 = 3 \times 3 \times 3 \\
&20 = 2 \times 2 \times 5 \\
&63 = 3 \times 3 \times 7 \\
&325 = 5 \times 5 \times 13 \\
&52 = 2 \times 2 \times 13 \\
&68 = 2 \times 2 \times 17 \\
&45 = 3 \times 3 \times 5 \\
&92 = 2 \times 2 \times 23 \\
&114 = 2 \times 3 \times 19
\end{aligned}
}
$$