Factors Worksheets | Printable Factors and Multiples Worksheets - Free Printable

Let's solve each problem step by step to find the prime factors of the given numbers using factor trees.

We'll break down each number into its prime factors, then write them in the format:
`_ x _ x _ = number`

---

1) 20

Start with 20:
- 20 can be split into 2 × 10
- 10 can be split into 2 × 5
- 2 and 5 are both prime numbers

So:
```
20
/ \
2 10
/ \
2 5
```

Prime Factors: 2 × 2 × 5 = 20
✔ Answer: `2 × 2 × 5 = 20`

---

2) 99

Start with 99:
- 99 can be split into 3 × 33
- 33 can be split into 3 × 11
- 3 and 11 are both prime numbers

```
99
/ \
3 33
/ \
3 11
```

Prime Factors: 3 × 3 × 11 = 99
✔ Answer: `3 × 3 × 11 = 99`

---

3) 45

Start with 45:
- 45 can be split into 5 × 9
- 9 can be split into 3 × 3
- 5 and 3 are both prime numbers

```
45
/ \
5 9
/ \
3 3
```

Prime Factors: 5 × 3 × 3 = 45
✔ Answer: `5 × 3 × 3 = 45`

---

4) 28

Start with 28:
- 28 can be split into 2 × 14
- 14 can be split into 2 × 7
- 2 and 7 are both prime numbers

```
28
/ \
2 14
/ \
2 7
```

Prime Factors: 2 × 2 × 7 = 28
✔ Answer: `2 × 2 × 7 = 28`

---

5) 52

Start with 52:
- 52 can be split into 2 × 26
- 26 can be split into 2 × 13
- 2 and 13 are both prime numbers

```
52
/ \
2 26
/ \
2 13
```

Prime Factors: 2 × 2 × 13 = 52
✔ Answer: `2 × 2 × 13 = 52`

---

6) 30

Start with 30:
- 30 can be split into 2 × 15
- 15 can be split into 3 × 5
- 2, 3, and 5 are all prime numbers

```
30
/ \
2 15
/ \
3 5
```

Prime Factors: 2 × 3 × 5 = 30
✔ Answer: `2 × 3 × 5 = 30`

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✔ Final Answers:

| Number | Prime Factorization |
|--------|---------------------|
| 1) 20 | 2 × 2 × 5 = 20 |
| 2) 99 | 3 × 3 × 11 = 99 |
| 3) 45 | 5 × 3 × 3 = 45 |
| 4) 28 | 2 × 2 × 7 = 28 |
| 5) 52 | 2 × 2 × 13 = 52 |
| 6) 30 | 2 × 3 × 5 = 30 |

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🔍 How to Fill the Diagrams (Factor Trees):

For each number:
- The top box is the original number.
- Split it into two factors (one should often be a small prime like 2, 3, 5).
- Keep splitting until all branches end in prime numbers.
- Write those primes in the circles.

Example for 20:
```
20
/ \
2 10
/ \
2 5
```
- Circles: 2, 2, 5
- Rectangle (middle): 10

You fill in the blanks accordingly.

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Let me know if you'd like this printed out or formatted as a completed worksheet!