Prime factor trees worksheet for Grade 5 students to practice finding prime factors.

Let's solve each of the prime factor trees step by step. The goal is to break down each number into its prime factors using a factor tree.

---

🔹 1. Factor Tree for 30

We are given:

```
30
/ \
5 [?]
```

We know that:
- 30 ÷ 5 = 6 → So, the other factor is 6

Now, break down 6 into two factors:
- 6 = 2 × 3 (both prime)

So, the complete tree looks like:

```
30
/ \
5 6
/ \
2 3
```

✔ Prime factors of 30: 2, 3, 5

---

🔹 2. Factor Tree for 81

Given:

```
81
/ \
[?] 9
```

We know:
- 81 ÷ 9 = 9 → So, the missing factor is 9

Now, break down 9:
- 9 = 3 × 3

So, both branches from 9 will be 3 and 3.

Now, we need to break down the top left 9 as well:
- 9 = 3 × 3

So the full tree:

```
81
/ \
9 9
/ \ / \
3 3 3 3
```

✔ Prime factors of 81: 3, 3, 3, 3 → or 3⁴

---

🔹 3. Factor Tree for 56

Given:

```
56
/ \
[?] [?]
```

Let’s find two factors of 56. A good choice is:
- 56 = 7 × 8

Now, break down 8:
- 8 = 2 × 4 → but 4 isn't prime, so further: 4 = 2 × 2

So let's build it:

```
56
/ \
7 8
/ \
2 4
/ \
2 2
```

But since the diagram has only three levels, we can do:

```
56
/ \
7 8
/ \
2 4
/ \
2 2
```

But wait — in the image, there are three circles under the 8, which suggests 8 is split into two factors, and one of those splits again.

Better: Start with:
- 56 = 8 × 7 → 8 is not prime, so split 8 into 2 × 4, then 4 into 2 × 2

So:

```
56
/ \
7 8
/ \
2 4
/ \
2 2
```

But the diagram shows:
- Top level: 56 → two boxes
- Then one box has two children, and the other has two children

Wait — looking at the structure:

It seems like:
- 56 splits into two numbers
- One of them splits into two (one prime, one composite)
- That composite splits again

So let’s try splitting 56 as 8 and 7 (as above), but perhaps better to split into 7 and 8, and then split 8 into 2 and 4, and 4 into 2 and 2

But in the diagram:

```
56
/ \
? ?
```

Then the right branch has:
- A box → then two boxes → one of which splits again?

Actually, the diagram shows:

```
56
/ \
o o
/ \
o o
/ \
o o
```

So it’s likely:
- 56 = 7 × 8
- 8 = 2 × 4
- 4 = 2 × 2

So fill in:

```
56
/ \
7 8
/ \
2 4
/ \
2 2
```

✔ Prime factors of 56: 2, 2, 2, 7 → or 2³ × 7

---

🔹 4. Factor Tree for 72

Given:

```
72
/ \
? ?
```

We need two factors of 72. Let’s pick:
- 72 = 8 × 9

Now:
- 8 = 2 × 4 → 4 = 2 × 2 → so 8 = 2 × 2 × 2
- 9 = 3 × 3

So:

```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```

But again, the diagram has:
- Two first-level branches
- Each splits into two
- One of the second-level branches splits again

So:

```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```

So the filled tree:

```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```

✔ Prime factors of 72: 2, 2, 2, 3, 3 → or 2³ × 3²

---

✔ Final Answers:

#### 1. 30
```
30
/ \
5 6
/ \
2 3
```
Prime factors: 2, 3, 5

#### 2. 81
```
81
/ \
9 9
/ \ / \
3 3 3 3
```
Prime factors: 3, 3, 3, 3 → 3⁴

#### 3. 56
```
56
/ \
7 8
/ \
2 4
/ \
2 2
```
Prime factors: 2, 2, 2, 7 → 2³ × 7

#### 4. 72
```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```
Prime factors: 2, 2, 2, 3, 3 → 2³ × 3²

---

📝 Summary Table:

| Number | Prime Factorization |
|--------|---------------------|
| 30 | 2 × 3 × 5 |
| 81 | 3⁴ |
| 56 | 2³ × 7 |
| 72 | 2³ × 3² |

Let me know if you'd like this formatted as a printable answer sheet!