Đáp án + Giải thích các bước giải:

Từ $\overline{abc}$ $\vdots$ 37 $\Rightarrow$ $\text{( 100a + 10b + c ) $\vdots$ 37}$

$\Rightarrow$ $\text{10 ( 100a + 10b + c ) $\vdots$ 37}$

$\Rightarrow$ $\text{( 1000a + 100b + 10c ) $\vdots$ 37}$

$\Rightarrow$ $\text{( 100b + 10c + a) + 999a $\vdots$ 37}$

$\Rightarrow$ $\text{$\overline{bca}$} + 999a $\vdots$ 37$

Vì 999 $\vdots$ 37 $\Rightarrow$ 999a $\vdots$ 37

Mà 999a + $\overline{bca}$ $\vdots$ 37

$\Rightarrow$ $\overline{bca}$ $\vdots$ 37 đpcm

Từ $\overline{abc}$ $\vdots$ 37 => ( 100a + 10 + c ) $\vdots$ 37

Từ $\overline{bca}$ $\vdots$ 37 $\Rightarrow$ $\text{( 100b + 10 + c) $\vdots$ 37}$

$\Rightarrow$ $\text{10 ( 100b + 10c a) $\vdots$ 37}$

$\Rightarrow$ $\text{( 1000b + 100c 10a ) $\vdots$ 37}$

$\Rightarrow$ $\text{( 100c + 10a + b) + 999b $\vdots$ 37}$

$\Rightarrow$ $\overline{cab}$ + 999b $\vdots$ 37

Vì 999 $\vdots$ 37 => 999b $\vdots$ 37

Mà $\overline{cab}$ + 999b $\vdots$ 37

$\Rightarrow$ $\overline{cab}$ $\vdots$ 37 đpcm

Đáp án + Giải thích các bước giải:

Ta có số `\overline{abc}`

`\overline{abc} \vdots 37`

`=> (100a + 10b + c) \vdots 37`

`=> 10 (100a + 10b + c) \vdots 37`

`=> (1000a + 100b + 10c) \vdots 37`

`=> (100 b + 10c + a + 999a) \vdots 37`

Mà: `999  \vdots 37`

`=> 999 a \vdots 37`

`=> (100b + 10c + a) \vdots 37`

`=> \overline{bca} \vdots 37 (đpcm)`

`(100b + 10c + a) \vdots 37`

`=> 10 ( 100b + 10c + a) \vdots 37`

`=> (1000b + 100c + 10a) \vdots 37`

`=> (100c + 10a + b + 999b) \vdots 37`

Mà:

`999 \vdots 37`

`=> 999 b \vdots 37`

`=> (100c + 10a + b) \vdots 37`

`=> \overline{cab} \vdots 37 (đpcm)`