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.

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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

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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 → not divisible 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

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✔ 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

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You can now fill in the ladder diagrams on the worksheet accordingly.

Let me know if you'd like a visual version or help printing it!