Factor Tree Worksheets - Math Worksheets - MathsDiary.com - Free Printable

Let's solve each factor tree step by step to find the prime factors of the given numbers: 70, 210, 132, and 300.

---

🔹 1. Factor Tree for 70

We are given:
```
70
/ \
7 ?
```

We know:
- 70 ÷ 7 = 10

So, the missing number is 10.

Now break down 10 into prime factors:
- 10 = 2 × 5

Both 2 and 5 are prime.

✔ So the completed tree:
```
70
/ \
7 10
/ \
2 5
```

Prime factors of 70: 2 × 5 × 7

---

🔹 2. Factor Tree for 210

Given:
```
210
/ \
? 6
```

We know:
- 210 ÷ 6 = 35

So, the missing number is 35

Now break down both:
- 6 = 2 × 3 (both prime)
- 35 = 5 × 7 (both prime)

✔ Completed tree:
```
210
/ \
35 6
/ \ / \
5 7 2 3
```

Prime factors of 210: 2 × 3 × 5 × 7

---

🔹 3. Factor Tree for 132

Given:
```
132
/ \
? ?
```

We need to split 132 into two factors. Let’s pick a small prime factor first.

- 132 is even → divisible by 2
- 132 ÷ 2 = 66

So:
```
132
/ \
2 66
```

Now break down 66:
- 66 ÷ 2 = 33 → so 66 = 2 × 33

Now 33 = 3 × 11 (both prime)

So full breakdown:
```
132
/ \
2 66
/ \
2 33
/ \
3 11
```

✔ Prime factors: 2 × 2 × 3 × 11 or 2² × 3 × 11

---

🔹 4. Factor Tree for 300

Given:
```
300
/ \
? ?
```

Break 300 into factors. Start with smallest prime:

- 300 is even → divide by 2 → 300 ÷ 2 = 150

So:
```
300
/ \
2 150
```

Now break 150:
- 150 ÷ 2 = 75 → so 150 = 2 × 75

Now 75 = 3 × 25

And 25 = 5 × 5

So full breakdown:
```
300
/ \
2 150
/ \
2 75
/ \
3 25
/ \
5 5
```

✔ Prime factors: 2 × 2 × 3 × 5 × 5 or 2² × 3 × 5²

---

✔ Final Answers (Completed Trees):

#### 1. 70
```
70
/ \
7 10
/ \
2 5
```
Prime factors: 2 × 5 × 7

#### 2. 210
```
210
/ \
35 6
/ \ / \
5 7 2 3
```
Prime factors: 2 × 3 × 5 × 7

#### 3. 132
```
132
/ \
2 66
/ \
2 33
/ \
3 11
```
Prime factors: 2 × 2 × 3 × 11

#### 4. 300
```
300
/ \
2 150
/ \
2 75
/ \
3 25
/ \
5 5
```
Prime factors: 2 × 2 × 3 × 5 × 5

---

📌 Summary Table:

| Number | Prime Factorization |
|--------|---------------------|
| 70 | 2 × 5 × 7 |
| 210 | 2 × 3 × 5 × 7 |
| 132 | 2² × 3 × 11 |
| 300 | 2² × 3 × 5² |

Let me know if you'd like this in printable format or want explanations on how to choose starting factors!