Sure! Let’s solve each problem by finding the
Greatest Common Factor (GCF) — also known as the Greatest Common Divisor (GCD) — of each pair of numbers. The GCF is the largest number that divides both numbers evenly.
We’ll go step-by-step for each problem.
---
1. GCF(40, 55)
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 55: 1, 5, 11, 55
- Common factors: 1, 5
✔ GCF = 5
---
2. GCF(33, 44)
- Factors of 33: 1, 3, 11, 33
- Factors of 44: 1, 2, 4, 11, 22, 44
- Common factors: 1, 11
✔ GCF = 11
---
3. GCF(30, 25)
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 25: 1, 5, 25
- Common factors: 1, 5
✔ GCF = 5
---
4. GCF(40, 18)
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2
✔ GCF = 2
---
5. GCF(20, 75)
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 75: 1, 3, 5, 15, 25, 75
- Common factors: 1, 5
✔ GCF = 5
---
6. GCF(12, 45)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 45: 1, 3, 5, 9, 15, 45
- Common factors: 1, 3
✔ GCF = 3
---
7. GCF(24, 9)
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 9: 1, 3, 9
- Common factors: 1, 3
✔ GCF = 3
---
8. GCF(45, 20)
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 5
✔ GCF = 5
---
9. GCF(36, 18)
- Since 18 divides 36 evenly (36 ÷ 18 = 2), the GCF is 18.
✔ GCF = 18
---
10. GCF(25, 35)
- Factors of 25: 1, 5, 25
- Factors of 35: 1, 5, 7, 35
- Common factors: 1, 5
✔ GCF = 5
---
##
✔ Final Answers:
1.
5
2.
11
3.
5
4.
2
5.
5
6.
3
7.
3
8.
5
9.
18
10.
5
---
💡
Tip: You can also use the
prime factorization method or
Euclidean algorithm for larger numbers, but for these small pairs, listing factors works perfectly!
Let me know if you’d like to see any of these solved using prime factorization too!
Parent Tip: Review the logic above to help your child master the concept of greatest common factor worksheet 6th grade.
