Question

BT3 :Chứng Minh

5) \(\overline{abcabc}\) \(⋮\) 7 ; 11 ; 13 ; 143

Answer 1

\(\overline{abcabc}=100000a+10000b+1000c+100a+10b+c\)

\(\overline{abcabc}=\left(100000+100\right)a+\left(10000+10\right)b+\left(1000+1\right)c\)

\(\overline{abcabc}=100100a+10010b+1001c\)

\(\overline{abcabc}=1001\left(100a+10b+c\right)\)

\(\Rightarrow\overline{abcabc}=143\left(100a+10b+c\right)⋮143\) (đpcm)

\(\Rightarrow\overline{abcabc}=13.7.11\left(100a+10b+c\right)⋮\begin{cases}11\\13\\7\end{cases}\)(đpcm)