Absolutely! Let's solve each problem step by step by listing the
factors of each number and then identifying the
greatest common factor (GCF) — which is the largest number that divides both numbers evenly.
---
1) Find the greatest common factor of 22 and 44.
Factors of 22:
We find all whole numbers that divide 22 without a remainder:
→ 1, 2, 11, 22
Factors of 44:
→ 1, 2, 4, 11, 22, 44
Common factors: 1, 2, 11, 22
Greatest common factor: →
22
✔ Answer: 22
---
2) Find the highest common factor of 45 and 27.
Factors of 45:
→ 1, 3, 5, 9, 15, 45
Factors of 27:
→ 1, 3, 9, 27
Common factors: 1, 3, 9
Highest common factor: →
9
✔ Answer: 9
---
3) Find the greatest common factor of 42 and 35.
Factors of 42:
→ 1, 2, 3, 6, 7, 14, 21, 42
Factors of 35:
→ 1, 5, 7, 35
Common factors: 1, 7
Greatest common factor: →
7
✔ Answer: 7
---
4) Find the highest common factor of 50 and 21.
Factors of 50:
→ 1, 2, 5, 10, 25, 50
Factors of 21:
→ 1, 3, 7, 21
Common factors: Only
1
Highest common factor: →
1
✔ Answer: 1
---
5) Find the greatest common divisor of 51 and 42.
*(Note: “Greatest common divisor” = “Greatest common factor”)*
Factors of 51:
→ 1, 3, 17, 51
Factors of 42:
→ 1, 2, 3, 6, 7, 14, 21, 42
Common factors: 1, 3
Greatest common divisor: →
3
✔ Answer: 3
---
##
✔ Final Answers:
1)
22
2)
9
3)
7
4)
1
5)
3
---
## 💡 Explanation Summary:
To find the
GCF (or GCD) using the
listing factors method:
- List
all positive factors of each number.
- Identify which factors appear in
both lists (common factors).
- Pick the
largest one from the common factors.
This method works well for smaller numbers and helps build understanding of what factors and common factors mean.
Let me know if you’d like to see how to solve these using prime factorization or the Euclidean algorithm too!
Parent Tip: Review the logic above to help your child master the concept of gcf worksheet pdf.
