Ta có: 108=33 x 22; 180=32 x 22 x 5
=> ƯCLN(108;180)=32 x 22=36
=> Ư (36)={1;2;4;6;9;12;18;36}
Vì x>15 => x={18;36}
Ta có : 108 chia hết cho x , 180 chia hết cho x \(\Rightarrow\)x thuộc ƯC { 180 ; 108 }
Mà 180 = 22 . 32 . 5 108 = 22 . 33
\(\Rightarrow\)ƯCLN ( 108 ; 180 ) = 22 . 32 = 36
\(\Rightarrow\)ƯC ( 108 ; 180 ) = Ư (36) = { 1 ; 2 ; 3 ; 4 ; 6 ; 9 ; 12 ; 18 ; 36 }
Vì x > 15 \(\Rightarrow\)x thuộc { 18 ; 36 }
Ta có \(108⋮x;180⋮x\Rightarrow x\inƯC\left(108;180\right)\)
Ta có: \(108=2^2.3^3;180;2^2.3^2.5\)\(\RightarrowƯCLN\left(108;180\right)=36\)\(\RightarrowƯC\left(108;180\right)=\left\{1;2;3;4;6;9;12;18;36\right\}\)
Mà \(x>15\Rightarrow x=\left\{18;36\right\}\)
Hok tốt!!