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

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 \times ? $
- $ 30 ÷ 5 = 6 $

So, the missing number is 6.

Now, break down 6:
- $ 6 = 2 \times 3 $ → both are prime

So, the completed tree:
```
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 other factor is 9

So:
```
81
/ \
9 9
```

Now break down each 9:
- $ 9 = 3 × 3 $

So:
```
81
/ \
9 9
/ \ / \
3 3 3 3
```

✔ Prime factors of 81: 3, 3, 3, 3 or $ 3^4 $

---

🔹 3. Factor Tree for 56

Given:
```
56
/ \
? ?
```

We need two numbers that multiply to 56. Let’s pick:
- $ 56 = 7 × 8 $ (since 7 is prime, good choice)

So:
```
56
/ \
7 8
```

Now break down 8:
- $ 8 = 2 × 4 $
- $ 4 = 2 × 2 $

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

✔ Prime factors of 56: 2, 2, 2, 7 or $ 2^3 × 7 $

---

🔹 4. Factor Tree for 72

Given:
```
72
/ \
? ?
```

Let’s break 72 into:
- $ 72 = 8 × 9 $ (both composite, but easy to factor)

So:
```
72
/ \
8 9
```

Break down:
- $ 8 = 2 × 4 $ → $ 4 = 2 × 2 $
- $ 9 = 3 × 3 $

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

So full tree:
```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```

✔ Prime factors of 72: 2, 2, 2, 3, 3 or $ 2^3 × 3^2 $

---

✔ 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 $ or $ 3^4 $

#### 3. 56
```
56
/ \
7 8
/ \
2 4
/ \
2 2
```
Prime factors: $ 2 × 2 × 2 × 7 $ or $ 2^3 × 7 $

#### 4. 72
```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```
Prime factors: $ 2 × 2 × 2 × 3 × 3 $ or $ 2^3 × 3^2 $

---

📝 Summary Table:

| Number | Prime Factorization |
|--------|---------------------|
| 30 | $ 2 × 3 × 5 $ |
| 81 | $ 3^4 $ |
| 56 | $ 2^3 × 7 $ |
| 72 | $ 2^3 × 3^2 $ |

You can now fill in the blanks on the worksheet accordingly!