\(\overline{abcdeg}=10000\overline{ab}+100\overline{cd}+\overline{eg}\\ =9999\overline{ab}+99\overline{cd}+\overline{ab}+\overline{cd}+\overline{eg}\\ =11\left(909\overline{ab}+9\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)\)
Mà \(\left\{{}\begin{matrix}11\left(909\overline{ab}+9\overline{cd}\right)⋮11\\\overline{ab}+\overline{cd}+\overline{eg}⋮11\end{matrix}\right.\Rightarrow11\left(909\overline{ab}+9\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)⋮11\)
\(\Rightarrow\overline{abcdeg}⋮11\)
\(\text{}\text{}\text{}\text{}\overline{abcdeg}=10000\overline{ab}+100\overline{cd}+\overline{eg}\)
\(=9999\overline{ab}+\overline{ab}+99\overline{cd}+\overline{cd}+\overline{eg}\)
\(=\left(9999\overline{ab}+99\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)\)
\(=11\left(909\overline{ab}+9\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)\vdots11\) ( Do \(11\left(909\overline{ab}+9\overline{cd}\right)\) và \(\overline{ab}+\overline{cd}+\overline{eg}\) đều chia hết cho \(11\) )
