What is the Highest Common Factor (HCF) of the fractions \frac{8}{15} and \frac{14}{25}? — State PSC Exam

What is the Highest Common Factor (HCF) of the fractions $\frac{8}{15}$ and $\frac{14}{25}$ ?

The Highest Common Factor (HCF) is

\frac{2}{75}

The correct answer is found by taking the Highest Common Factor (HCF) of the numerators (

8

and

14

), which is

2

, and dividing it by the Least Common Multiple (LCM) of the denominators (

15

and

25

), which is

75

. This yields exactly

\frac{2}{75}

Identify the numerators and denominators of the given fractions.

The numerators are

8

and

14

. The denominators are

15

and

25

The formula for the HCF of fractions requires processing numerators and denominators separately.

Calculate the Highest Common Factor (HCF) of the numerators.

The HCF of

8

and

14

2

According to the formula, the numerator of the final answer must be the HCF of the original numerators.

Calculate the Least Common Multiple (LCM) of the denominators.

The LCM of

15

and

25

75

According to the formula, the denominator of the final answer must be the LCM of the original denominators.

Combine the results into a single fraction.

The resulting fraction is

\frac{2}{75}

The HCF of fractions is defined as

\frac{\text{HCF of numerators}}{\text{LCM of denominators}}

Highest Common Factor (HCF) of Fractions

Question