To find the Greatest Common Factor (GCF) using the ladder method, we divide both numbers by common factors until there are no more common factors left. Then, we multiply all the numbers on the left side of the ladder to get the GCF.
Let’s solve each problem step by step:
---
Problem 2: (24, 36)
Step 1: Divide both by 2 → 24 ÷ 2 = 12, 36 ÷ 2 = 18
Step 2: Divide both by 2 again → 12 ÷ 2 = 6, 18 ÷ 2 = 9
Step 3: Divide both by 3 → 6 ÷ 3 = 2, 9 ÷ 3 = 3
Now, 2 and 3 have no common factors.
Ladder:
2 | 24 36
2 | 12 18
3 | 6 9
| 2 3
GCF = 2 × 2 × 3 =
12
---
Problem 3: (25, 45)
Step 1: Divide both by 5 → 25 ÷ 5 = 5, 45 ÷ 5 = 9
Now, 5 and 9 have no common factors.
Ladder:
5 | 25 45
| 5 9
GCF =
5
---
Problem 4: (40, 60)
Step 1: Divide both by 2 → 40 ÷ 2 = 20, 60 ÷ 2 = 30
Step 2: Divide both by 2 again → 20 ÷ 2 = 10, 30 ÷ 2 = 15
Step 3: Divide both by 5 → 10 ÷ 5 = 2, 15 ÷ 5 = 3
Now, 2 and 3 have no common factors.
Ladder:
2 | 40 60
2 | 20 30
5 | 10 15
| 2 3
GCF = 2 × 2 × 5 =
20
---
Problem 5: (30, 60)
Step 1: Divide both by 2 → 30 ÷ 2 = 15, 60 ÷ 2 = 30
Step 2: Divide both by 3 → 15 ÷ 3 = 5, 30 ÷ 3 = 10
Step 3: Divide both by 5 → 5 ÷ 5 = 1, 10 ÷ 5 = 2
Now, 1 and 2 have no common factors.
Ladder:
2 | 30 60
3 | 15 30
5 | 5 10
| 1 2
GCF = 2 × 3 × 5 =
30
*(Note: Since 30 is a factor of 60, the GCF is just 30.)*
---
Problem 6: (25, 55)
Step 1: Divide both by 5 → 25 ÷ 5 = 5, 55 ÷ 5 = 11
Now, 5 and 11 have no common factors.
Ladder:
5 | 25 55
| 5 11
GCF =
5
---
Final Answers:
2. 12
3. 5
4. 20
5. 30
6. 5
Final Answer:
2. 12
3. 5
4. 20
5. 30
6. 5
Parent Tip: Review the logic above to help your child master the concept of factoring using gcf worksheet.
