Let's solve the
Factor Tree Worksheet step by step. The goal is to break down each number into its
prime factors using a factor tree, and then fill in the apples at the bottom with the
prime factors.
---
🔹 Understanding the Example:
The example shows:
-
100
- 100 → 2 × 50
- 50 → 2 × 25
- 25 → 5 × 5
- So prime factors are:
2, 2, 5, 5
- Apples show:
2, 2, 5, 5
So we do the same for the other numbers.
---
##
✔ Problem 1:
54
We start factoring 54:
1.
54 = 2 × 27 (since 54 is even)
2.
27 = 3 × 9
3.
9 = 3 × 3
So the full factor tree:
```
54
/ \
2 27
/ \
3 9
/ \
3 3
```
Prime factors:
2, 3, 3, 3
✔ Apples should be:
2, 3, 3, 3
---
##
✔ Problem 2:
81
81 is odd, not divisible by 2.
1.
81 = 9 × 9
2.
9 = 3 × 3, so:
- 81 = 3 × 3 × 3 × 3
Or:
```
81
/ \
9 9
/ \ / \
3 3 3 3
```
Prime factors:
3, 3, 3, 3
✔ Apples:
3, 3, 3, 3
---
##
✔ Problem 3:
72
Break down 72:
1.
72 = 8 × 9
- Or better:
72 = 2 × 36
2.
36 = 6 × 6 → or
36 = 2 × 18
- Let’s go step by step:
- 72 → 2 × 36
- 36 → 2 × 18
- 18 → 2 × 9
- 9 → 3 × 3
So:
```
72
/ \
2 36
/ \
2 18
/ \
2 9
/ \
3 3
```
Prime factors:
2, 2, 2, 3, 3
✔ Apples:
2, 2, 2, 3, 3
---
##
✔ Problem 4:
450
Start factoring:
1.
450 is even, so divide by 2:
- 450 = 2 × 225
2.
225 is odd, ends in 5 → divisible by 5:
- 225 = 5 × 45
3. 45 = 5 × 9
4. 9 = 3 × 3
So:
```
450
/ \
2 225
/ \
5 45
/ \
5 9
/ \
3 3
```
Prime factors:
2, 5, 5, 3, 3
✔ Apples:
2, 3, 3, 5, 5
---
📌 Final Answers:
#### 1.
54
- Factor Tree:
```
54
/ \
2 27
/ \
3 9
/ \
3 3
```
- Apples:
2, 3, 3, 3
#### 2.
81
- Factor Tree:
```
81
/ \
9 9
/ \ / \
3 3 3 3
```
- Apples:
3, 3, 3, 3
#### 3.
72
- Factor Tree:
```
72
/ \
2 36
/ \
2 18
/ \
2 9
/ \
3 3
```
- Apples:
2, 2, 2, 3, 3
#### 4.
450
- Factor Tree:
```
450
/ \
2 225
/ \
5 45
/ \
5 9
/ \
3 3
```
- Apples:
2, 3, 3, 5, 5
---
✔ Summary of Apple Answers:
| Number | Prime Factors (Apples) |
|--------|-------------------------|
| 54 | 2, 3, 3, 3 |
| 81 | 3, 3, 3, 3 |
| 72 | 2, 2, 2, 3, 3 |
| 450 | 2, 3, 3, 5, 5 |
> 💡
Tip: Always start with the smallest prime (2), then move to 3, 5, 7, etc., until all branches end in prime numbers.
Let me know if you'd like this as a printable answer sheet! 🍎🌳
Parent Tip: Review the logic above to help your child master the concept of factor tree example.
