Question

[minamoto mimiko]

Chứng minh rằng nếu \(\overline{ab}=2.\overline{cd}\)thì \(\overline{abcd}⋮67\)

Answer 1

[TBQT]

Ta có : \(\overline{abcd}=10\overline{ab}+\overline{cd}=100.2.\overline{cd}+\overline{cd}\)

                    \(=201.\overline{cd}\)

Mà      \(201⋮67\)nên \(201.\overline{cd}⋮67\)

Vậy \(\overline{abcd}⋮67\)

Answer 2

[Shinichi Kudo]

Ta có: abcd = ab x 100 + cd =200cd +cd (vì ab = 2cd)

hay=201cd

Mà \(201⋮67\left(=3\right)\)

\(\Rightarrow201\overline{cd}⋮67\)

Vậy \(\overline{ab}=2\overline{cd}\Leftrightarrow\overline{abcd}⋮67\)