Question

The H.C.F. of the fractions $\frac{8}{21},\frac{12}{35},\frac{32}{7}$ is

Answer 1

The fractions $\frac{8}{21},\frac{12}{35},\frac{32}{7}$

Step 1 HCF of numerators

$$\begin{gathered} 8=2^3 \\ 12=2^2\times 3 \\ 32=2^5 \\ HCF(8,12,32)=2^2=4 \end{gathered}$$

Step 2 HCF of denominators

$$\begin{gathered} 21=3\times 7 \\ 35=5\times 7 \\ 7=1\times 7 \\ LCM(21,35,7)=3\times 5\times 7=105 \end{gathered}$$

$HCFofafraction=\frac{HCFofnumerator}{LCMofdenominator}$

HCF of fraction$=\frac{4}{105}$