Question

Can the number $6^n$, $n$ being a natural number, end with the digit $5$4 ? Give reason.

Answer 1

The number is $6^n$, $nϵN$
$6^n$ to be end in $5$, it should be divisible by $5$.
$6^n=(2\ast 3{)}^n$
The prime factors of $6^n$ are $2$ and $3$.
$\therefore 6^n$ cannot end with the digit $5$.