Find the Greatest Common Factor (GCF) using the ladder method in this math worksheet.

Let's solve each problem using the ladder method to find the Greatest Common Factor (GCF). The ladder method involves dividing both numbers by common prime factors until no more common factors exist, then multiplying all the common divisors used.

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1. (20, 30)

This one is already solved in the image:

```
2 | 20 30
5 | 10 15
| 2 3
```

- Divide by 2: 20 ÷ 2 = 10, 30 ÷ 2 = 15
- Divide by 5: 10 ÷ 5 = 2, 15 ÷ 5 = 3
- No more common factors

So, GCF = 2 × 5 = 10

✔ Correct!

---

2. (24, 36)

We'll use the ladder method:

```
2 | 24 36
2 | 12 18
3 | 6 9
| 2 3
```

- Divide by 2: 24 ÷ 2 = 12, 36 ÷ 2 = 18
- Divide by 2 again: 12 ÷ 2 = 6, 18 ÷ 2 = 9
- Divide by 3: 6 ÷ 3 = 2, 9 ÷ 3 = 3
- Now 2 and 3 have no common factors

So, GCF = 2 × 2 × 3 = 12

✔ Answer: 12

---

3. (25, 45)

```
5 | 25 45
| 5 9
```

- Divide by 5: 25 ÷ 5 = 5, 45 ÷ 5 = 9
- 5 and 9 have no common factors

So, GCF = 5

✔ Answer: 5

---

4. (40, 60)

```
2 | 40 60
2 | 20 30
2 | 10 15
5 | 2 3
| 1 1
```

- Divide by 2: 40 ÷ 2 = 20, 60 ÷ 2 = 30
- Divide by 2: 20 ÷ 2 = 10, 30 ÷ 2 = 15
- Divide by 2: 10 ÷ 2 = 5, 15 ÷ 2? → Wait! 15 is not divisible by 2.

Wait — we made a mistake here.

Actually:
- After first 2: 20, 30
- Second 2: 10, 15 → now 10 is even, 15 is odd → can't divide by 2 again.
- But 10 and 15 are both divisible by 5?

Yes! Let's correct:

```
2 | 40 60
2 | 20 30
5 | 10 15
| 2 3
```

- Divide by 2: 40 → 20, 60 → 30
- Divide by 2: 20 → 10, 30 → 15
- Divide by 5: 10 → 2, 15 → 3
- 2 and 3 have no common factors

So, GCF = 2 × 2 × 5 = 20

✔ Answer: 20

---

5. (30, 60)

```
2 | 30 60
3 | 15 30
5 | 5 10
| 1 2
```

- Divide by 2: 30 → 15, 60 → 30
- Divide by 3: 15 → 5, 30 → 10
- Divide by 5: 5 → 1, 10 → 2
- Now 1 and 2 → no common factor

So, GCF = 2 × 3 × 5 = 30

✔ Answer: 30

---

6. (25, 55)

```
5 | 25 55
| 5 11
```

- Divide by 5: 25 ÷ 5 = 5, 55 ÷ 5 = 11
- 5 and 11 have no common factors

So, GCF = 5

✔ Answer: 5

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✔ Final Answers:

| Problem | Numbers | GCF |
|--------|---------|-----|
| 1 | (20, 30) | 10 |
| 2 | (24, 36) | 12 |
| 3 | (25, 45) | 5 |
| 4 | (40, 60) | 20 |
| 5 | (30, 60) | 30 |
| 6 | (25, 55) | 5 |

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🔍 Summary of Ladder Method Steps:

1. Write the two numbers side by side.
2. Divide both by a common prime factor.
3. Write the quotients below.
4. Repeat with new pair until no common factors remain.
5. Multiply all the divisors on the left → that’s your GCF.

Let me know if you'd like this as a printable worksheet or need visual diagrams!