a) \large\frac{3}{14}

b) \large\frac{7}{14}

c) \large\frac{9}{14}

d) \large\frac{5}{14}

correct answer is: a) \large\frac{3}{14}

#### Explanation

Here, Product of two fractions is \large\frac{27}{98}

And, their LCM be 1\large\frac{2}{7} or \large\frac{9}{7}

We know,

LCM \times HCF = Product of Two Numbers

\rightarrow\large\frac{9}{7}\times HCF =\large\frac{27}{98}

\rightarrow HCF =\large\frac{27}{98}\div\large\frac{9}{7}

\rightarrow HCF =\large\frac{27}{98}\times\large\frac{7}{9}

\rightarrow HCF =\large\frac{3}{14}

\therefore Their HCF is \large\frac{3}{14} **Ans:** HCF \large\frac{3}{14}.

###### Other variants of this math particular question are:

**Finding the highest common factor of fractions resulting in 27/98 when multiplied, given their LCM as 1 2/7.****What is the greatest common factor of two fractions whose multiplication yields 27/98, and their least common multiple is 1 2/7?****Find the greatest common divisor of two fractions resulting in 27/98 when multiplied, given their least common multiple as 1 2/7.**