Question : The HCF of $\frac{1}{2}, \frac{3}{4}, \frac{5}{6},$ and $\frac{7}{8}$ is:
Option 1: $\frac{105}{2}$
Option 2: $\frac{1}{24}$
Option 3: $\frac{7}{24}$
Option 4: $\frac{1}{48}$
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Correct Answer: $\frac{1}{24}$
Solution :
Given: $\frac{1}{2}, \frac{3}{4}, \frac{5}{6},$ and $\frac{7}{8}$
HCF of fractions = $\frac{\text{HCF of numerators}}{\text{LCM of denominators}}$
= $\frac{\text{HCF of 1,3,5,7}}{\text{LCM of 2,4,6,8}}$
= $\frac{1}{24}$
Hence, the correct answer is $\frac{1}{24}$.
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