Prime factor trees worksheet for finding prime factors of numbers using tree diagrams.

Let's solve the Prime Factor Tree worksheet step by step. The goal is to find the prime factors of each number using a factor tree method.

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🔹 What is a Prime Factor Tree?

A prime factor tree breaks down a number into its prime factors (numbers divisible only by 1 and themselves) by repeatedly dividing it into smaller factors until all branches end in prime numbers.

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We’ll go through each number:

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1. 15

- 15 = 3 × 5
- Both 3 and 5 are prime.
✔ Prime factors: 3 and 5

```
15
/ \
3 5
```

So, 15 = 3 × 5

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2. 21

- 21 = 3 × 7
- Both 3 and 7 are prime.
✔ Prime factors: 3 and 7

```
21
/ \
3 7
```

So, 21 = 3 × 7

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3. 25

- 25 = 5 × 5
- 5 is prime.
✔ Prime factors: 5 and 5

```
25
/ \
5 5
```

So, 25 = 5 × 5 or 5²

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4. 35

- 35 = 5 × 7
- Both 5 and 7 are prime.
✔ Prime factors: 5 and 7

```
35
/ \
5 7
```

So, 35 = 5 × 7

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5. 49

- 49 = 7 × 7
- 7 is prime.
✔ Prime factors: 7 and 7

```
49
/ \
7 7
```

So, 49 = 7 × 7 or 7²

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6. 51

- 51 = 3 × 17
- 3 and 17 are both prime.
✔ Prime factors: 3 and 17

```
51
/ \
3 17
```

So, 51 = 3 × 17

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7. 55

- 55 = 5 × 11
- Both 5 and 11 are prime.
✔ Prime factors: 5 and 11

```
55
/ \
5 11
```

So, 55 = 5 × 11

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8. 57

- 57 = 3 × 19
- Both 3 and 19 are prime.
✔ Prime factors: 3 and 19

```
57
/ \
3 19
```

So, 57 = 3 × 19

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9. 65

- 65 = 5 × 13
- Both 5 and 13 are prime.
✔ Prime factors: 5 and 13

```
65
/ \
5 13
```

So, 65 = 5 × 13

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✔ Final Answers:

| Number | Prime Factorization |
|--------|---------------------|
| 15 | 3 × 5 |
| 21 | 3 × 7 |
| 25 | 5 × 5 |
| 35 | 5 × 7 |
| 49 | 7 × 7 |
| 51 | 3 × 17 |
| 55 | 5 × 11 |
| 57 | 3 × 19 |
| 65 | 5 × 13 |

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📝 Instructions for Filling the Worksheet:

For each box:
- Fill in the two circles under the number with its two factors (that multiply to give the number).
- Make sure both are prime, or continue factoring if not.
- Then write the full prime factorization below.

Example for 15:
```
15
/ \
3 5
```
Then write: 15 = 3 × 5

Repeat for all others.

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