To find the set of factors for the numbers 88, 105, and 96, we can use the prime factorization method. Here’s a step-by-step solution for each number:
### (i) Factors of 88
1. **Start with the number 88.**
2. **Divide by the smallest prime number (2):**
- 88 ÷ 2 = 44
3. **Continue dividing by 2:**
- 44 ÷ 2 = 22
4. **Continue dividing by 2:**
- 22 ÷ 2 = 11
5. **11 is a prime number, so we divide by 11:**
- 11 ÷ 11 = 1
6. **List all the factors:**
- From the divisions, we can find the factors:
- 1, 2, 4 (2×2), 8 (2×2×2), 11, 22 (2×11), 44 (4×11), 88 (8×11).
**Set of factors of 88:** {1, 2, 4, 8, 11, 22, 44, 88}
### (ii) Factors of 105
1. **Start with the number 105.**
2. **Divide by the smallest prime number (3):**
- 105 ÷ 3 = 35
3. **Next, divide by 5:**
- 35 ÷ 5 = 7
4. **7 is a prime number, so we divide by 7:**
- 7 ÷ 7 = 1
5. **List all the factors:**
- From the divisions, we can find the factors:
- 1, 3, 5, 7, 15 (3×5), 21 (3×7), 35 (5×7), 105 (3×5×7).
**Set of factors of 105:** {1, 3, 5, 7, 15, 21, 35, 105}
### (iii) Factors of 96
1. **Start with the number 96.**
2. **Divide by the smallest prime number (2):**
- 96 ÷ 2 = 48
3. **Continue dividing by 2:**
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
4. **3 is a prime number, so we divide by 3:**
- 3 ÷ 3 = 1
5. **List all the factors:**
- From the divisions, we can find the factors:
- 1, 2, 3, 4 (2×2), 6 (2×3), 8 (2×2×2), 12 (4×3), 16 (2×2×2×2), 24 (8×3), 32 (16×2), 48 (24×2), 96 (48×2).
**Set of factors of 96:** {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}
### Summary of Factors
- Factors of 88: {1, 2, 4, 8, 11, 22, 44, 88}
- Factors of 105: {1, 3, 5, 7, 15, 21, 35, 105}
- Factors of 96: {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}
