To solve the problem of finding the greatest common factor (GCF) for each pair of numerals, we will use the method of prime factorization. Here's a step-by-step explanation and solution for each pair:
---
1) 2, 8
-
Prime factorization:
- \( 2 = 2 \)
- \( 8 = 2 \times 2 \times 2 \)
-
Common factors: The only common factor is \( 2 \).
-
GCF: \( 2 \)
Answer: GCF =
2
---
2) 10, 30
-
Prime factorization:
- \( 10 = 2 \times 5 \)
- \( 30 = 2 \times 3 \times 5 \)
-
Common factors: The common factors are \( 2 \) and \( 5 \).
-
GCF: \( 2 \times 5 = 10 \)
Answer: GCF =
10
---
3) 24, 50
-
Prime factorization:
- \( 24 = 2 \times 2 \times 2 \times 3 \)
- \( 50 = 2 \times 5 \times 5 \)
-
Common factors: The only common factor is \( 2 \).
-
GCF: \( 2 \)
Answer: GCF =
2
---
4) 4, 48
-
Prime factorization:
- \( 4 = 2 \times 2 \)
- \( 48 = 2 \times 2 \times 2 \times 2 \times 3 \)
-
Common factors: The common factors are \( 2 \times 2 = 4 \).
-
GCF: \( 4 \)
Answer: GCF =
4
---
5) 16, 32
-
Prime factorization:
- \( 16 = 2 \times 2 \times 2 \times 2 \)
- \( 32 = 2 \times 2 \times 2 \times 2 \times 2 \)
-
Common factors: The common factors are \( 2 \times 2 \times 2 \times 2 = 16 \).
-
GCF: \( 16 \)
Answer: GCF =
16
---
6) 6, 21
-
Prime factorization:
- \( 6 = 2 \times 3 \)
- \( 21 = 3 \times 7 \)
-
Common factors: The only common factor is \( 3 \).
-
GCF: \( 3 \)
Answer: GCF =
3
---
7) 33, 44
-
Prime factorization:
- \( 33 = 3 \times 11 \)
- \( 44 = 2 \times 2 \times 11 \)
-
Common factors: The only common factor is \( 11 \).
-
GCF: \( 11 \)
Answer: GCF =
11
---
8) 21, 35
-
Prime factorization:
- \( 21 = 3 \times 7 \)
- \( 35 = 5 \times 7 \)
-
Common factors: The only common factor is \( 7 \).
-
GCF: \( 7 \)
Answer: GCF =
7
---
9) 20, 45
-
Prime factorization:
- \( 20 = 2 \times 2 \times 5 \)
- \( 45 = 3 \times 3 \times 5 \)
-
Common factors: The only common factor is \( 5 \).
-
GCF: \( 5 \)
Answer: GCF =
5
---
10) 18, 27
-
Prime factorization:
- \( 18 = 2 \times 3 \times 3 \)
- \( 27 = 3 \times 3 \times 3 \)
-
Common factors: The common factors are \( 3 \times 3 = 9 \).
-
GCF: \( 9 \)
Answer: GCF =
9
---
Final Answers:
1. GCF =
2
2. GCF =
10
3. GCF =
2
4. GCF =
4
5. GCF =
16
6. GCF =
3
7. GCF =
11
8. GCF =
7
9. GCF =
5
10. GCF =
9
Boxed Final Answer:
\[
\boxed{2, 10, 2, 4, 16, 3, 11, 7, 5, 9}
\]
Parent Tip: Review the logic above to help your child master the concept of common factor worksheet.
