If $n \equiv 43 \pmod{60}$, then what is the residue of $n$ modulo 6?

$$\small{\text{
If $n \equiv 43 \pmod{60}$, then what is the residue of $n$ modulo 6?
}}$$

$$\small{\text{$
\begin{array}{lrcl}
(1) & n - 43 &=& 60\\
(2) & n-x &=& m\cdot 6 \\
\\
\hline
\\
(1)-(2) & n-43 - n + x &=& 60 - m\cdot 6 \\
& -43 + x &=& 60 - m\cdot 6 \\
&x &=& 60+43- m\cdot 6 \\
&x &=& 103- m\cdot 6 \qquad | \qquad m =17 \mathrm{~~lowest
~positive ~integer}\\
&x &=& 103-102\\
& \mathbf{x} & \mathbf{=} & \mathbf{1 }
\end{array}
$}}\\$$

the residue of n modulo 6 is 1