Printable math worksheet for practicing finding the Greatest Common Factor using the ladder method.

Let's solve each problem using the ladder method to find the Greatest Common Factor (GCF).

---

🔷 What is the Ladder Method?

The ladder method involves:
1. Writing the two numbers side by side.
2. Dividing both numbers by a common prime factor (starting with the smallest).
3. Writing the quotients below.
4. Repeating until no more common factors exist.
5. Multiplying all the common prime factors on the left side of the "ladder" — that’s the GCF.

---

We’ll go through each pair:

---

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

✔ Answer: 10

---

2. (24, 36)

Let’s build the ladder:

```
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.

Common prime factors: 2, 2, 3

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.

Common factor: 5

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 = 7.5 → Wait! 15 is not divisible by 2.

Wait — correction: After 20 and 30, divide by 2:
20 ÷ 2 = 10, 30 ÷ 2 = 15 → OK

Now 10 and 15: both divisible by 5?

Wait — let's fix it step-by-step:

Actually:
- 40 and 60 → both divisible by 2 → 20, 30
- 20 and 30 → both divisible by 2 → 10, 15
- 10 and 15 → both divisible by 5 → 2, 3
- 2 and 3 → no common factors

So ladder:

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

Common factors: 2, 2, 5

GCF = 2 × 2 × 5 = 20

✔ Answer: 20

---

5. (30, 60)

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

Wait — check divisibility:

- 30 and 60 → divisible by 2 → 15, 30
- 15 and 30 → divisible by 3 → 5, 10
- 5 and 10 → divisible by 5 → 1, 2

Now 1 and 2 → no common factors

So:

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

Common factors: 2, 3, 5

GCF = 2 × 3 × 5 = 30

✔ Answer: 30

---

6. (25, 55)

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

- 25 and 55 → divisible by 5 → 5, 11
- 5 and 11 → no common factors

So only common factor: 5

GCF = 5

✔ Answer: 5

---

✔ Final Answers:

| Problem | Pair | 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 |

---

📝 Summary:

You use the ladder method by dividing both numbers by common prime factors until they can't be divided further. Multiply all the divisors on the left side to get the GCF.

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