Question

If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to :

• A. 14
• B. 6
• C. 4
• D. 8

Answer 1

Answer: (D)

$\frac{2^{403}}{15}=\frac{2^3.{\left(2^4\right)}^{100}}{15}=\frac{8}{15}{\left(15+1\right)}^{100}$
$=\frac{8}{15}\left(15\lambda +1\right)=8\lambda +\frac{8}{15}$
$\because 8\lambda$ is integer
$\Rightarrow$ fractional part of $\frac{2^{403}}{15}\frac{8}{15}\Rightarrow k=8$