Fill in the missing numbers in the prime factor trees to complete the factorization.

Let's solve Factor Tree Worksheet 1 step by step. The goal is to complete each factor tree by breaking down the given number into its prime factors, using multiplication facts.

---

🔍 Understanding Factor Trees

A factor tree breaks a number down into its prime factors. We start with the given number and split it into two factors (not necessarily prime), then continue splitting until all branches end in prime numbers.

We use the rule:
> If a number is divisible by a smaller number, we can split it accordingly.

Let’s go through each problem:

---

1) 30

Start with 30.
We know:
30 = 6 × 5 → but 6 is not prime.
Better:
30 = 2 × 15
→ 15 = 3 × 5

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

✔ Prime factors: 2, 3, 5

Answer:
- First branch: 2 and 15
- Then 15 splits into 3 and 5

Fill in:
- Left: 2
- Right: 15
- Below 15: 3 and 5

---

2) 24

24 = 8 × 3 → 8 is not prime
Or: 24 = 4 × 6 → both composite
Best: 24 = 2 × 12
→ 12 = 2 × 6
→ 6 = 2 × 3

So:
```
24
/ \
2 12
/ \
2 6
/ \
2 3
```

But since we only need two levels, we can do:

24 = 2 × 12
Then 12 = 3 × 4? No — better: 12 = 2 × 6 or 3 × 4

Let’s use:
24 = 3 × 8
→ 8 = 2 × 4 → 4 = 2 × 2

Alternatively, simpler path:
24 = 4 × 6
→ 4 = 2 × 2
→ 6 = 2 × 3

But standard way:
24 = 2 × 12
→ 12 = 3 × 4 → 4 = 2 × 2

Wait — better to pick prime as one of the first splits.

Best:
24 = 2 × 12
→ 12 = 2 × 6
→ 6 = 2 × 3

So:
```
24
/ \
2 12
/ \
2 6
/ \
2 3
```

But again, if only two levels, maybe they expect:

24 = 3 × 8
→ 8 = 2 × 4 → not ideal

Or:
24 = 4 × 6
→ 4 = 2 × 2
→ 6 = 2 × 3

But let's assume the worksheet wants any valid factorization, then break further.

But looking at the diagram:
It has three circles below, so likely:

Top: 24
Then two branches: ? and ?
Then those split into two more.

So we need to split 24 into two factors (not necessarily prime), then split each into primes.

Try:
24 = 6 × 4
→ 6 = 2 × 3
→ 4 = 2 × 2

So:
```
24
/ \
6 4
/ \ / \
2 3 2 2
```

Yes! This works.

Fill in:
- Left: 6
- Right: 4
- Below 6: 2 and 3
- Below 4: 2 and 2

✔ So answer: 6 and 4

---

3) 33

33 = 3 × 11 → both prime

So:
```
33
/ \
3 11
```

No further splitting needed.

So:
- Left: 3
- Right: 11

✔ Answer: 3 and 11

---

4) 12

12 = 3 × 4
→ 4 = 2 × 2

Or: 12 = 2 × 6
→ 6 = 2 × 3

Either works.

Let’s use: 12 = 2 × 6
→ 6 = 2 × 3

So:
```
12
/ \
2 6
/ \
2 3
```

Answer:
- Left: 2
- Right: 6
- Below 6: 2 and 3

✔

---

5) 30 (again)

Same as #1.

30 = 2 × 15
→ 15 = 3 × 5

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

Answer: 2 and 15 → then 3 and 5

✔

---

6) 27

27 = 3 × 9
→ 9 = 3 × 3

So:
```
27
/ \
3 9
/ \
3 3
```

Answer: 3 and 9 → then 3 and 3

✔

---

7) 10

10 = 2 × 5 → both prime

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

Answer: 2 and 5

✔

---

8) 18

18 = 2 × 9
→ 9 = 3 × 3

So:
```
18
/ \
2 9
/ \
3 3
```

Answer: 2 and 9 → then 3 and 3

✔

---

9) 45

45 = 5 × 9
→ 9 = 3 × 3

Or: 45 = 3 × 15 → 15 = 3 × 5

Let’s use: 45 = 5 × 9
→ 9 = 3 × 3

So:
```
45
/ \
5 9
/ \
3 3
```

Answer: 5 and 9 → then 3 and 3

✔

---

✔ Final Answers:

| Problem | Top Number | First Split (Left) | First Split (Right) | Second Split (Left) | Second Split (Right) |
|--------|------------|---------------------|----------------------|----------------------|-----------------------|
| 1) | 30 | 2 | 15 | 3 | 5 |
| 2) | 24 | 6 | 4 | 2 | 2 |
| 3) | 33 | 3 | 11 | – | – |
| 4) | 12 | 2 | 6 | 2 | 3 |
| 5) | 30 | 2 | 15 | 3 | 5 |
| 6) | 27 | 3 | 9 | 3 | 3 |
| 7) | 10 | 2 | 5 | – | – |
| 8) | 18 | 2 | 9 | 3 | 3 |
| 9) | 45 | 5 | 9 | 3 | 3 |

> Note: For problems where the second level is already prime (like 33, 10), no further splitting is needed.

---

📝 Summary of How to Fill the Worksheet

For each box:
- Write the two factors of the top number.
- Then write the prime factors of each non-prime factor.

Use common factor pairs that are easy to work with.

---

Let me know if you'd like this formatted for printing or as a filled-in PDF!