Question

The remainder when $6^{504}$ is divided by $215$ is

• A. $2$
• B. $1$
• C. $214$
• D. None of these

Answer 1

The correct option is B $1$

$6^3=216$

$\Rightarrow 6^{504}={\left(6^3\right)}^{168}$

$={(215+1)}^{168}$

$=\left[{{}^{168}C}_0\right(215{)}^{168}+.....{{}^{168}C}_1\left(215\right)+1]$

$\Rightarrow 6^{504}=215\lambda +1$ ; $\lambda \in I.$

$\therefore$ Where $6^{504}$ is divided by $215$, we get the quotient as $\lambda$ & remainder $=1$

Hence the answer is $1.$