Tìm số tự nhiên a , biết 398 chia a dư 38 còn 450 chia a dư 18

Vì : 398 chia cho a dư 38 \(\Rightarrow398-38⋮a\Rightarrow360⋮a\) ( a > 38 ) (1)

Vì : 450 chia cho a dư 18 \(\Rightarrow450-18⋮a\Rightarrow432⋮a\) ( a > 18 ) (2)

Từ (1) và (2)

\(\Rightarrow a\inƯC\left(360,432\right)\left(a>38\right)\)

\(360=2^3.3^2.5\)

\(432=2^4.3^3\)

\(ƯCLN\left(360,432\right)=2^3.3^2=72\)

\(ƯC\left(360,432\right)=\left\{1;2;3;4;8;24;36;72\right\}\)

Mà : a > 38 => a = 72

Vậy a = 72

398 : a dư 38 =>398-38=360 chia hết cho a

450 : a dư 18 =>450-18=432 chia hết cho a

Điều kiện a thuộc N^*

Ta tìm ƯCLN của 360 và 432:

360=2³.3².5

432=2⁴.3³

Suy ra ƯCLN của 360 và 432 = 2³.3²=8.9=72

Vậy a=72

Zu la la

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Ta c : 

398 : a du 38 

=> 398 - 38 =360 chia het cho a

450 a du 18 

=> 450 - 18 = 432 chia het cho a

Dieu kien a thuoc N*

Ta co UCLN(360;432)

360=2³.3².5

432=2⁴.3³

Suy ra : UCLN(360;432)=2³.3²=71

Vay a=71

**** nhe

398 chia a dư 38 => 398-38 = 360 chia hết cho a

450 chia a dư 18 => 450-18 = 432 chia hết cho a 

Với a thuộc N*

Ta có: ƯCLN(360,432) = 72

Vậy a = 72