Question

What is the greatest common divisor of $\frac{2}{3}$, $\frac{4}{5}$ and $\frac{8}{9}$ ?

• A. $\frac{1}{45}$
• B. $\frac{8}{45}$
• C. $\frac{2}{45}$
• D. $\frac{45}{2}$

Answer 1

The correct option is C

$\frac{2}{45}$

The greatest common divisor (GCD) of two or more numbers is the greatest number which divides each of them exactly. It is similar to HCF.
HCF (GCD) of fractions $=\frac{\text{HCF of numerators}}{\text{LCM of denominators}}$
HCF of numerators 2, 4, and 8 = 2
LCM of denominators 3, 5, and 9 = 45
$\therefore$ HCF (GCD) of the given numbers $=\frac{2}{45}$