Chứng minh rằng nếu 2. ab = cd thì abcd ⋮ 3 .

Ta có: \(\overline {abcd} \, = 100\overline {ab} \, + \,\overline {cd} \)

Suy ra  \(\overline {abcd} \, = 50.\,\overline {cd} \, + \,\overline {cd} \) (vì \(2.\overline {ab} \, = \overline {cd} \))

Do đó \(\overline {abcd} \, = 51.\,\overline {cd} \,\)

Nên \(\overline {abcd} \, = 3.17.\,\overline {cd} \,\)

Suy ra \(\overline {abcd} \vdots \,3\)(đpcm)