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)

8

Answer 2

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