Question

If $31z5$ is a multiple of $9$, where $z$ is a digit. Find the smallest value of $z$.

Answer 1

Since $31z5$ is a multiple of $9$.
Sum of the digits $3+1+z+5=9+z$ is a multiple of $9$. So, $9+z$ is either $0$ or $9$, $18$, $27$...and so on. Since $z$ is a digit
This is possible when $9+z=9$ or $18$ or $27$ and so on..
$\Rightarrow z=9-9$
$\Rightarrow z=0$
If $9+z=18$
$\Rightarrow z=18-9=9$
Thus, the two possible values are $0$ and $9$.

smallest is $0$