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)

$8$

$\frac{2^{403}}{15}=\frac{2^3\cdot (2^4{)}^{100}}{15}=\frac{8}{15}(15+1{)}^{100}$

$=\frac{8}{15}(15\lambda +1)=8\lambda +\frac{8}{15}$

$\because 8\lambda$ is integer

$\Rightarrow$ fractional part of $\frac{2^{403}}{15}$ is $\frac{8}{15}\Rightarrow k=8$.