Math worksheet for 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).

The ladder method means:
- Write the two numbers side by side.
- Divide both by a common factor (start with small primes like 2, 3, 5…).
- Write the results below.
- Keep dividing until the numbers at the bottom have no common factors other than 1.
- Multiply all the divisors on the left — that’s your GCF.

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Problem 2: (24, 36)

Step 1: Both divisible by 2
→ 24 ÷ 2 = 12
→ 36 ÷ 2 = 18

Step 2: 12 and 18 still divisible by 2
→ 12 ÷ 2 = 6
→ 18 ÷ 2 = 9

Step 3: 6 and 9 divisible by 3
→ 6 ÷ 3 = 2
→ 9 ÷ 3 = 3

Now we have 2 and 3 — no common factors except 1. Stop.

Divisors used: 2, 2, 3
GCF = 2 × 2 × 3 = 12

✔ Check: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Biggest common factor is 12 → Correct!

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Problem 3: (25, 45)

Step 1: Both divisible by 5
→ 25 ÷ 5 = 5
→ 45 ÷ 5 = 9

Now we have 5 and 9 — no common factors except 1. Stop.

Divisor used: 5
GCF = 5

✔ Check: Factors of 25: 1, 5, 25
Factors of 45: 1, 3, 5, 9, 15, 45
Biggest common factor is 5 → Correct!

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Problem 4: (40, 60)

Step 1: Both divisible by 2
→ 40 ÷ 2 = 20
→ 60 ÷ 2 = 30

Step 2: 20 and 30 divisible by 2
→ 20 ÷ 2 = 10
→ 30 ÷ 2 = 15

Step 3: 10 and 15 divisible by 5
→ 10 ÷ 5 = 2
→ 15 ÷ 5 = 3

Now we have 2 and 3 — stop.

Divisors: 2, 2, 5
GCF = 2 × 2 × 5 = 20

✔ Check: Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Biggest common factor is 20 → Correct!

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Problem 5: (30, 60)

Step 1: Both divisible by 2
→ 30 ÷ 2 = 15
→ 60 ÷ 2 = 30

Step 2: 15 and 30 divisible by 3
→ 15 ÷ 3 = 5
→ 30 ÷ 3 = 10

Step 3: 5 and 10 divisible by 5
→ 5 ÷ 5 = 1
→ 10 ÷ 5 = 2

Now we have 1 and 2 — stop.

Divisors: 2, 3, 5
GCF = 2 × 3 × 5 = 30

✔ Check: 30 divides into 60 exactly twice → So GCF is 30 → Correct!

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Problem 6: (25, 55)

Step 1: Both divisible by 5
→ 25 ÷ 5 = 5
→ 55 ÷ 5 = 11

Now we have 5 and 11 — no common factors except 1. Stop.

Divisor used: 5
GCF = 5

✔ Check: Factors of 25: 1, 5, 25
Factors of 55: 1, 5, 11, 55
Biggest common factor is 5 → Correct!

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Final Answer:
2. 12
3. 5
4. 20
5. 30
6. 5