Certainly! To find the greatest common factor (GCF) for each pair of numbers, let's carefully consider each pair and determine the GCF through their individual prime factorizations. Here’s the step-by-step approach:
### 1. Pair (6, 15)
- Factorize 6: [tex]\(6 = 2 \times 3\)[/tex]
- Factorize 15: [tex]\(15 = 3 \times 5\)[/tex]
- Common factors: [tex]\(3\)[/tex]
- GCF: [tex]\(3\)[/tex]
### 2. Pair (20, 24)
- Factorize 20: [tex]\(20 = 2^2 \times 5\)[/tex]
- Factorize 24: [tex]\(24 = 2^3 \times 3\)[/tex]
- Common factors: [tex]\(2^2\)[/tex]
- GCF: [tex]\(2^2 = 4\)[/tex]
### 3. Pair (32, 14)
- Factorize 32: [tex]\(32 = 2^5\)[/tex]
- Factorize 14: [tex]\(14 = 2 \times 7\)[/tex]
- Common factors: [tex]\(2\)[/tex]
- GCF: [tex]\(2\)[/tex]
### 4. Pair (9, 21)
- Factorize 9: [tex]\(9 = 3^2\)[/tex]
- Factorize 21: [tex]\(21 = 3 \times 7\)[/tex]
- Common factors: [tex]\(3\)[/tex]
- GCF: [tex]\(3\)[/tex]
### 5. Pair (35, 15)
- Factorize 35: [tex]\(35 = 5 \times 7\)[/tex]
- Factorize 15: [tex]\(15 = 3 \times 5\)[/tex]
- Common factors: [tex]\(5\)[/tex]
- GCF: [tex]\(5\)[/tex]
### 6. Pair (18, 27)
- Factorize 18: [tex]\(18 = 2 \times 3^2\)[/tex]
- Factorize 27: [tex]\(27 = 3^3\)[/tex]
- Common factors: [tex]\(3^2\)[/tex]
- GCF: [tex]\(3^2 = 9\)[/tex]
### 7. Pair (4, 12)
- Factorize 4: [tex]\(4 = 2^2\)[/tex]
- Factorize 12: [tex]\(12 = 2^2 \times 3\)[/tex]
- Common factors: [tex]\(2^2\)[/tex]
- GCF: [tex]\(2^2 = 4\)[/tex]
### 8. Pair (15, 40)
- Factorize 15: [tex]\(15 = 3 \times 5\)[/tex]
- Factorize 40: [tex]\(40 = 2^3 \times 5\)[/tex]
- Common factors: [tex]\(5\)[/tex]
- GCF: [tex]\(5\)[/tex]
So, let's summarize the GCFs for each pair:
1. Pair (6, 15) - GCF: 3
2. Pair (20, 24) - GCF: 4
3. Pair (32, 14) - GCF: 2
4. Pair (9, 21) - GCF: 3
5. Pair (35, 15) - GCF: 5
6. Pair (18, 27) - GCF: 9
7. Pair (4, 12) - GCF: 4
8. Pair (15, 40) - GCF: 5
