Question

The total number of non-trivial positive divisors of $2^3{3}^k$ are $28$. Then $k=$

Answer 1

The total number of non-trivial divisors of $2^3{3}^k$ will be $=(3+1)(k+1)=4(k+1)$
$\therefore 4(k+1)=28$
$\Rightarrow k+1=7$
$\Rightarrow k=6$