Giải:
\(36=4.9\)
Để số \(\overline{1x8y2}⋮36\) Điều kiện: \(\left\{{}\begin{matrix}0\le x,y\le9\\x,y\in N\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(1+x+8+y+2\right)⋮9\\\overline{1x8y2}⋮4\Leftrightarrow\overline{y2}⋮4\end{matrix}\right.\)
Ta có:
\(\overline{y2}⋮4\Leftrightarrow y=\left\{1;3;5;7;9\right\}\)
\(\left(1+x+8+y+2\right)⋮9\Leftrightarrow\left(x+y+2\right)⋮9\)
\(\Rightarrow\left[{}\begin{matrix}x+y=7\\x+y=16\end{matrix}\right.\) \(\Leftrightarrow x=\left\{6;4;2;0;9;7\right\}\)
Mà \(\left(4;9\right)=1\) nên ta có các số cần tìm:
\(16812;14832;12852;10872;19872;17892\)