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Tìm số tự nhiên n nhỏ nhất biết khi chia cho 11, 17, 29 được số dư là 6, 12, 24

a) Tìm số tự nhiên n nhỏ nhất biết khi chia cho 11; 17; 29 thì số dư lần lượt là 6; 12; 24

b) Tìm số tự nhiên nhỏ nhất có chữ số tận cùng là 7; chia 13 dư 8; chia 19 dư 14

Theo dõi Vi phạm
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  • a) n chia 11 dư 6, chia 17 dư 12, chia 29 dư 24 => n chia 11;17;29 đều thiếu 5

    =>n+5 chia hết cho 11;17;29

    Vì n nhỏ nhất =>n+5 là BCNN(11;17;29)

    Vì 11;17;29 nguyên tố cùng nhau

    =>n+5= BCNN(11;17;29)=11x17x29=5423

    =>n=5423-5=5418

    b) Gọi số tự nhiên cần tìm là x

    x chia 13 dư 8, chia 19 dư 14 => x chia 13;19 đều thiếu 5

    => x+5 chia hết cho 13;19 Vì x nhỏ nhất => x+5 là BCNN(13;19)

    Vì 13;19 nguyên tố cùng nhau

    => x+5=BCNN(13;19)=13x19=247

    => x+5 thuộc B(247)={0;247;494;741;988;1235;1482;...}

    Để có số tận cùng là 7 => x+5 tận cùng là 2 => x+5=1482

    x=1482-5

    x=1477

      bởi Thai duy Khuong 19/12/2018
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