Factors Worksheets | Printable Factors and Multiples Worksheets - Free Printable

To solve the problem of finding the prime factors of the given numbers, we will use the method of factor trees. The goal is to break down each number into its prime factors step by step.

Step-by-Step Solution:

#### 1) Number: 20
- Start with 20.
- Break it down into two factors: \( 20 = 4 \times 5 \).
- Further break down 4 into \( 2 \times 2 \).
- The number 5 is already a prime number.
- So, the prime factors of 20 are \( 2 \times 2 \times 5 \).

Factor Tree:
```
20
/ \
4 5
/ \
2 2
```

Prime Factors: \( 2 \times 2 \times 5 \)

#### 2) Number: 99
- Start with 99.
- Break it down into two factors: \( 99 = 9 \times 11 \).
- Further break down 9 into \( 3 \times 3 \).
- The number 11 is already a prime number.
- So, the prime factors of 99 are \( 3 \times 3 \times 11 \).

Factor Tree:
```
99
/ \
9 11
/ \
3 3
```

Prime Factors: \( 3 \times 3 \times 11 \)

#### 3) Number: 45
- Start with 45.
- Break it down into two factors: \( 45 = 9 \times 5 \).
- Further break down 9 into \( 3 \times 3 \).
- The number 5 is already a prime number.
- So, the prime factors of 45 are \( 3 \times 3 \times 5 \).

Factor Tree:
```
45
/ \
9 5
/ \
3 3
```

Prime Factors: \( 3 \times 3 \times 5 \)

#### 4) Number: 28
- Start with 28.
- Break it down into two factors: \( 28 = 4 \times 7 \).
- Further break down 4 into \( 2 \times 2 \).
- The number 7 is already a prime number.
- So, the prime factors of 28 are \( 2 \times 2 \times 7 \).

Factor Tree:
```
28
/ \
4 7
/ \
2 2
```

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

#### 5) Number: 52
- Start with 52.
- Break it down into two factors: \( 52 = 4 \times 13 \).
- Further break down 4 into \( 2 \times 2 \).
- The number 13 is already a prime number.
- So, the prime factors of 52 are \( 2 \times 2 \times 13 \).

Factor Tree:
```
52
/ \
4 13
/ \
2 2
```

Prime Factors: \( 2 \times 2 \times 13 \)

#### 6) Number: 30
- Start with 30.
- Break it down into two factors: \( 30 = 6 \times 5 \).
- Further break down 6 into \( 2 \times 3 \).
- The number 5 is already a prime number.
- So, the prime factors of 30 are \( 2 \times 3 \times 5 \).

Factor Tree:
```
30
/ \
6 5
/ \
2 3
```

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

Final Answers:

1. Prime Factors of 20: \( \boxed{2 \times 2 \times 5} \)
2. Prime Factors of 99: \( \boxed{3 \times 3 \times 11} \)
3. Prime Factors of 45: \( \boxed{3 \times 3 \times 5} \)
4. Prime Factors of 28: \( \boxed{2 \times 2 \times 7} \)
5. Prime Factors of 52: \( \boxed{2 \times 2 \times 13} \)
6. Prime Factors of 30: \( \boxed{2 \times 3 \times 5} \)