$\overline{abcmnp}=6\times \overline{mnpabc}$
$\overline{abc}\times 1000+\overline{mnp}=6\times \left( \overline{mnp}\times 1000+\overline{abc} \right)$
$1000\times \overline{abc}-6\times \overline{abc}=6000\times \overline{mnp}-\overline{mnp}$
$994\times \overline{abc}=5999\times \overline{mnp}$
$142\times \overline{abc}=857\times \overline{mnp}$
Vì $857\times \overline{mnp}$chia hết cho 857 nên $142\times \overline{abc}$chia hết cho 857
Mà $142$ không chia hết cho 857 nên $\overline{abc}$ chia hết cho 857
$\Rightarrow \overline{abc}=142$
$\Rightarrow \overline{mnp}=142$