Tìm số $\overline{abc}$ sao cho : $\left\{\begin{array}{l}(\overline{abc}-5)\vdots 8\\(\overline{abc}-6)\vdots 11\end{array}\right.$

Question

Tìm số $\overline{abc}$ sao cho : $\left\{\begin{array}{l}(\overline{abc}-5)\vdots 8\\(\overline{abc}-6)\vdots 11\end{array}\right.$

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Daisy 3 tuần 2021-08-23T18:58:55+00:00 1 Answers 0 views 0

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    2021-08-23T19:00:29+00:00

    Đáp án:

    \(\overline {abc} \) ∈ {149,237,325,413,501,589,677,765,853,941}

    Giải thích các bước giải:

    (\(\overline {abc} \)-5) chia hết cho 8

    -> (\(\overline {abc} \)-5+4.8)=(\(\overline {abc} \)+27) chia hết cho 8

    (\(\overline {abc} \)-6) chia hết cho 11

    -> (\(\overline {abc} \)-6+3.11)=(\(\overline {abc} \)+27) chia hết cho 11

    -> (\(\overline {abc} \)+27) chia hết cho 8,11

    -> (\(\overline {abc} \)+27) ∈ BC(8,11)

    BCNN (8,11)=88

    -> (\(\overline {abc} \)+27) ∈ BC(8,11)=(88,176,264,352,440,528,616,704,792,880,968,1056,..}

    mà \(\overline {abc} \) là số có 3 chữ số

    -> \(\overline {abc} \) ∈ {149,237,325,413,501,589,677,765,853,941}

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