remainder

Let this number be $x$ . We are given that

$x=342k+47 \quad k\in\mathbb{Z}$

So to find the remainder when $x$ is divided by $19$

$\begin{aligned} x &\equiv 342k+47\\ &\equiv 18\cdot\mathbin{\color{#D61F06} 19}\cdot k + 2\cdot\mathbin{\color{#3D99F6} 19}+9\\ &\equiv 18\cdot\mathbin{\color{#D61F06}0}\cdot k + 2\cdot\mathbin{\color{#3D99F6}0}+9\\ &\equiv \boxed{9} \mod{19} \end{aligned}$