Prime Factorization Worksheets - 15 Worksheets Library - Free Printable

You're working on Prime Factorization using the Ladder Method — a visual and systematic way to break down a number into its prime factors.

Let me solve each problem step by step, showing the ladder method and writing the final prime factorization.

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🔢 1) 64 — Already Solved (for reference)

Ladder:
```
2 | 64
2 | 32
2 | 16
2 | 8
2 | 4
2 | 2
| 1
```

✔ Prime Factorization:
64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

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🔢 2) 80

Start dividing by the smallest prime (2), then continue with primes until you reach 1.

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

✔ Prime Factorization:
80 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5

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🔢 3) 90

Divide by 2 first (since 90 is even), then by 3, etc.

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

✔ Prime Factorization:
90 = 2 × 3 × 3 × 5 = 2 × 3² × 5

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🔢 4) 72

Divide by 2, then keep going.

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

✔ Prime Factorization:
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

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🔢 5) 120

Start with 2, then 2 again, then 2, then 3, then 5.

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

✔ Prime Factorization:
120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5

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🔢 6) 150

Even → divide by 2, then 3, then 5.

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

✔ Prime Factorization:
150 = 2 × 3 × 5 × 5 = 2 × 3 × 5²

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## ✔ Final Answers to Fill In:

2) 80 = 2 × 2 × 2 × 2 × 5
*(or 2⁴ × 5)*

3) 90 = 2 × 3 × 3 × 5
*(or 2 × 3² × 5)*

4) 72 = 2 × 2 × 2 × 3 × 3
*(or 2³ × 3²)*

5) 120 = 2 × 2 × 2 × 3 × 5
*(or 2³ × 3 × 5)*

6) 150 = 2 × 3 × 5 × 5
*(or 2 × 3 × 5²)*

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## 🧠 How the Ladder Method Works:

1. Write the number at the top.
2. Divide by the smallest prime number that divides it evenly.
3. Write the quotient below.
4. Repeat with the quotient until you get 1.
5. The prime factors are all the numbers on the left side of the ladder.

It’s like climbing down a ladder — each step is a division by a prime!

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Let me know if you want to see this drawn out visually or need help with more numbers! 😊