Question

Check whether $(15{)}^n$ can end with digit O for any $nϵN$

Answer 1

If ${15}^n$ is divisible by 10 then it can end with digit zero.

If it is divisible by 10, it has to be divisible by 5 and 2 both.

The prime factorization of 15 is $3\times 5$.

${15}^n=(3\times 5{)}^n$

By observation, $(3\times 5{)}^n$ is divisible by 5 but not by 2.

Hence, ${15}^n$ is not divisible by 10.

Hence, ${15}^n$ does not end with digit 0 for any natural number n.