Question

CMR :

Nếu abc ⋮ 27 thì bca ⋮ 27

Answer 1

\(\overline{abc}⋮27\)

=>\(100a+10b+c⋮27\)

=>\(81a+19a+10b+c⋮27\)

=>\(19a+10b+c⋮27\)

\(\overline{bca}=100b+10c+a=81b+19a+10b+c+\left(9b+9c-18a\right)\)

=>\(\overline{bca}=81b+\left(19a+10b+c\right)+9\left(b+c-2a\right)\)

\(b+c-2a=b+c+a-3a⋮3\)(Vì \(\overline{abc}\) chia hết cho 27 nên a+b+c chia hết cho 3)

=>9(b+c-2a) chia hết cho 27

=>\(\overline{bca}\) chia hết cho 27(ĐPCM)