The H.C.F. of $\frac{a}{b}, \frac{c}{d}, \frac{e}{f}$ is equal to

### Concept & Formula This is a direct theoretical question testing the formula for finding the Highest Common Factor (HCF) of fractions. To find the HCF of a set of fractions, you take the HCF of their numerators and divide it by the LCM of their denominators. $$\text{H.C.F. of fractions} = \frac{\text{H.C.F. of Numerators}}{\text{L.C.M. of Denominators}}$$ ### Step-by-Step Solution * **Given Fractions:** $\frac{a}{b}$, $\frac{c}{d}$, and $\frac{e}{f}$ * **Numerators:** $a, c, e$ * **Denominators:** $b, d, f$ * **Apply the formula:** $$\text{Result} = \frac{\text{H.C.F. of } (a, c, e)}{\text{L.C.M. of } (b, d, f)}$$ * This directly matches option (b). ### Exam Strategy & Shortcut There is no calculation required here. A simple memory trick for fractions: **The operation requested for the fractions is the same operation performed on the numerators.** * If asked for **HCF** of fractions $\rightarrow$ Put **HCF** on top. * If asked for **LCM** of fractions $\rightarrow$ Put **LCM** on top. ### Common Pitfall The most common mistake is swapping the numerator and denominator operations (selecting option (a)), which is the formula for finding the L.C.M. of fractions, not the H.C.F. ### Final Answer **Therefore, the correct answer is $\frac{\text{H.C.F. of } a, c, e}{\text{L.C.M. of } b, d, f}$.**