Question

If the fractional part of the number 2^403/15is k/15, then k is equal to :

Answer 1

Given that,

$\dfrac{2^{403}}{15}=\dfrac{k}{15}$

To find,

The value of k.

Solution,

We have,

$\dfrac{2^{403}}{15}=\dfrac{k}{15}$

So,

$\dfrac{2^{403}}{15}=2^3\times 2^{400}\\\\=8\times 2^{4\times 100}\\\\=8\times (2^4)^{100}\\\\=8\times 16^{100}\\\\=8(1+15)^{100}$

Using binomial expansion,

$=8(1+15k)\\\\2^{403}=8+120k\\\\\dfrac{2^{403}}{15}=\dfrac{8}{15}+\dfrac{120k}{15}$

Hence, it would mean that the remainder is 8. So, the value of k is equal to 8.

Answer 2

Answer is k=8....

question is  

If the fractional part of the number 2^403/15is k/15, then k is equal to :