Question

What is the last digit of $6^{100}$.

Answer 1

$6^1,6^2,6^3,6^4,6^5.................{.6}^{99},6^{100}$.
$6^1=6$,
$6^2=6\ast 6=36$,
$6^3=6\ast 6\ast 6=216$.
Since, $6^n$ for any positive ${}^{\prime }{n}^{\prime }$ ends with $6$.
$\therefore$ The unit of $6^n$ is always $6$.
$\therefore$ The last digit of $6^{100}$ is also $6$.