\(\overline{abcd}⋮\overline{ab}.\overline{cd}\Rightarrow\overline{abcd}⋮\overline{ab};\overline{cd}\)
\(\overline{abcd}=ab\cdot100+cd\)
\(\overline{abcd}⋮ab\Rightarrow\overline{cd}⋮\overline{ab}\Rightarrow\overline{cd}=m\cdot\overline{ab}\)(m là chữ số do ad;cd là có 2 chữ số )
\(\overline{abcd}⋮\overline{cd}\Rightarrow\overline{ab}\cdot100⋮\overline{cd}\Rightarrow100\cdot\overline{ab}=n\cdot\overline{cd}\)
\(100\cdot\overline{ab}=m\cdot n\cdot\overline{ab}\Rightarrow m\cdot n=100\Rightarrow m=1;2;4;5\)
\(\left(+\right)m=1\Rightarrow\overline{ab}=\overline{cd}\): \(\overline{abcd}=\overline{abab}⋮\overline{ab}\cdot\overline{ab}\Rightarrow101\cdot\overline{ab}⋮\overline{ab}\cdot\overline{ab}\Rightarrow101⋮\overline{ab}\)
không có số nào thỏa mãn
\(\left(+\right)m=2\Rightarrow\overline{cd}=2\cdot\overline{ab}\): \(\overline{abcd}=100\overline{ab}+2\overline{ab}=102\cdot\overline{ab}⋮2\cdot\overline{ab}\cdot\overline{ab}\Rightarrow51⋮\overline{ab}\)
\(\Rightarrow\overline{ab}=17;\overline{cd}=34\)
\(\Rightarrow=1734\)
\(\left(+\right)m=4\Rightarrow\overline{cd}=4\cdot\overline{ab}\): \(\overline{abcd}=104\cdot\overline{ab}⋮4\cdot\overline{ab}\cdot\overline{ab}\Rightarrow26⋮\overline{ab}\)
\(\Rightarrow\overline{ab}=13;\overline{cd}=52\)
\(\Rightarrow1352\)
\(\left(+\right)m=5\Rightarrow\overline{cd}=5\cdot\overline{ab}\):\(\overline{abcd}=105\cdot\overline{ab}⋮5\cdot\overline{ab}\cdot\overline{ab}\Rightarrow21⋮\overline{ab}\)
\(\Rightarrow\overline{ab}=21;\overline{cd}=105\)ko chia hết ( loại )
vậy ta có 2 số thỏa mãn : 1734 và 1352
