Prime Factorization Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of the prime factorization problems using the Ladder Method. The ladder method involves dividing the number by prime numbers (starting with the smallest, like 2, then 3, 5, etc.) until we get down to 1.

---

1) 64

Already solved:
```
2 | 64
2 | 32
2 | 16
2 | 8
2 | 4
| 2
```

So:
64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

✔ Correct.

---

2) 80

We divide 80 by the smallest prime (2):

```
2 | 80
2 | 40
2 | 20
2 | 10
5 | 5
| 1
```

So:
80 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5

---

3) 90

Start with 2:

- 90 ÷ 2 = 45 → not divisible by 2 anymore
- Try 3: 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1

```
2 | 90
3 | 45
3 | 15
5 | 5
| 1
```

So:
90 = 2 × 3 × 3 × 5 = 2 × 3² × 5

---

4) 72

Divide by 2:

- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

```
2 | 72
2 | 36
2 | 18
3 | 9
3 | 3
| 1
```

So:
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

---

5) 120

Start with 2:

- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1

```
2 | 120
2 | 60
2 | 30
3 | 15
5 | 5
| 1
```

So:
120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5

---

6) 150

Start with 2:

- 150 ÷ 2 = 75 → can't divide by 2 anymore
- Try 3: 75 ÷ 3 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

```
2 | 150
3 | 75
5 | 25
5 | 5
| 1
```

So:
150 = 2 × 3 × 5 × 5 = 2 × 3 × 5²

---

✔ Final Answers:

1) 64 = 2⁶
2) 80 = 2⁴ × 5
3) 90 = 2 × 3² × 5
4) 72 = 2³ × 3²
5) 120 = 2³ × 3 × 5
6) 150 = 2 × 3 × 5²

---

📝 How to Fill in the Ladder Diagrams:

For each problem, write the divisor on the left and the quotient below the original number, continuing until you reach 1.

#### Example for 80:
```
2 | 80
2 | 40
2 | 20
2 | 10
5 | 5
| 1
```
Then write: 80 = 2 × 2 × 2 × 2 × 5

Repeat similarly for others.

Let me know if you'd like a printable version or visual diagram!