(Highest common factor of 18, 24 and 36) / (Highest common factor of 16, 26, 48) is equal to

Options

A. 1
B. 2
C. 4
D. 3

Answer

To solve the question, we need to find the highest common factor (HCF) of two sets of numbers and then divide the HCF of the first set by the HCF of the second set.

### Step-by-Step Solution:

1. **Find the HCF of 18, 24, and 36:**
- **Prime Factorization:**
- 18 = 2 × 3 × 3 = 2 × 3²
- 24 = 2 × 2 × 2 × 3 = 2³ × 3
- 36 = 2 × 3 × 3 = 2 × 3²
- **Identify Common Factors:**
- The common prime factors are 2 and 3.
- The lowest power of 2 in all three numbers is 2¹.
- The lowest power of 3 in all three numbers is 3¹.
- **Calculate HCF:**
- HCF = 2¹ × 3¹ = 2 × 3 = 6.

2. **Find the HCF of 16, 26, and 48:**
- **Prime Factorization:**
- 16 = 2 × 2 × 2 × 2 = 2⁴
- 26 = 2 × 13 = 2¹ × 13¹
- 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3¹
- **Identify Common Factors:**
- The only common prime factor is 2.
- The lowest power of 2 in all three numbers is 2¹.
- **Calculate HCF:**
- HCF = 2¹ = 2.

3. **Divide the HCF of the first set by the HCF of the second set:**
- We have HCF(18, 24, 36) = 6 and HCF(16, 26, 48) = 2.
- Now, divide:
- \( \frac{HCF(18, 24, 36)}{HCF(16, 26, 48)} = \frac{6}{2} = 3 \).

### Final Answer:
The result of the division is 3.

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