Fill in the Apples | Math Factor Tree Worksheets for 4th Grade - Free Printable

Let's solve each of the factor trees in Section A step by step, finding the prime factor decomposition of each number and expressing it in index notation.

We'll follow the same method as shown in the example:

---

🔹 1. 36

Start with 36.

- 36 = 2 × 18 → 2 is prime (blue), 18 is not (orange)
- 18 = 2 × 9 → 2 is prime, 9 is not
- 9 = 3 × 3 → both are prime

So:
```
36
/ \
2 18
/ \
2 9
/ \
3 3
```

Prime factors: 2, 2, 3, 3
→ $ 36 = 2^2 \times 3^2 $

✔ Answer: $ 36 = 2^2 \times 3^2 $

---

🔹 2. 54

Start with 54.

- 54 = 2 × 27 → 2 is prime, 27 is not
- 27 = 3 × 9 → 3 is prime, 9 is not
- 9 = 3 × 3 → both prime

```
54
/ \
2 27
/ \
3 9
/ \
3 3
```

Prime factors: 2, 3, 3, 3
→ $ 54 = 2 \times 3^3 $

✔ Answer: $ 54 = 2 \times 3^3 $

---

🔹 3. 135

Start with 135.

- 135 = 5 × 27 → 5 is prime, 27 is not
- 27 = 3 × 9 → 3 is prime, 9 is not
- 9 = 3 × 3 → both prime

```
135
/ \
5 27
/ \
3 9
/ \
3 3
```

Prime factors: 5, 3, 3, 3
→ $ 135 = 3^3 \times 5 $

✔ Answer: $ 135 = 3^3 \times 5 $

---

🔹 4. 525

Start with 525.

- 525 = 5 × 105 → 5 is prime, 105 is not
- 105 = 5 × 21 → 5 is prime, 21 is not
- 21 = 3 × 7 → both prime

```
525
/ \
5 105
/ \
5 21
/ \
3 7
```

Prime factors: 5, 5, 3, 7
→ $ 525 = 3 \times 5^2 \times 7 $

✔ Answer: $ 525 = 3 \times 5^2 \times 7 $

---

🔹 5. 693

Start with 693.

- 693 = 3 × 231 → 3 is prime, 231 is not
- 231 = 3 × 77 → 3 is prime, 77 is not
- 77 = 7 × 11 → both prime

```
693
/ \
3 231
/ \
3 77
/ \
7 11
```

Prime factors: 3, 3, 7, 11
→ $ 693 = 3^2 \times 7 \times 11 $

✔ Answer: $ 693 = 3^2 \times 7 \times 11 $

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## ✔ Final Answers:

| Number | Prime Factor Decomposition (Index Notation) |
|--------|---------------------------------------------|
| 36 | $ 2^2 \times 3^2 $ |
| 54 | $ 2 \times 3^3 $ |
| 135 | $ 3^3 \times 5 $ |
| 525 | $ 3 \times 5^2 \times 7 $ |
| 693 | $ 3^2 \times 7 \times 11 $ |

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📌 Summary of How to Solve:

1. Start with the number at the top.
2. Break it into two factors: one prime (blue circle), one composite (orange).
3. Keep breaking down the composite numbers until all branches end in prime numbers.
4. List all the prime numbers at the bottom.
5. Write them in index form (e.g., $ 2^4 $).

Let me know if you'd like this filled in on the worksheet format!