Question

chứng minh rằng :      

abc - cba chia hết cho 99

Answer 1

$\iff 100a+10b+c-100c-10b-a=99a-99c=99(a-c)$

 

=> abc - cba chia hết cho 99

Answer 2

Ta có : \(\overline{abc}-\overline{cba}=\left(100a+10b+c\right)-\left(100c+10b+a\right)\)

\(=\left(100a-a\right)+\left(10b-10b\right)-\left(100c-c\right)\)

\(=99a-99c=99\left(a-c\right)\) chia hết cho 99

 

Answer 3

\(\overline{abc}-\overline{cba}=\left(100a+10b+c\right)-\left(100c+10b+a\right)=99a-99c=99\left(a-c\right)\)Vì 99(a - c) \(⋮\) 99 \(\Rightarrow\) \(\overline{abc}-\overline{cba}\) \(⋮\) 99

\(\Rightarrow\) Điều phải chứng minh

Answer 4

abc-cba 
=100a+10b+c-100c-10b-a 
=99a-99c chia hết cho 99

Answer 5

$\iff 100a+10b+c-100c-10b-a=99a-99c=99(a-c)$ 

=> abc -cbachia hết cho 99