\(\text{153 chia x dư 3 }\Rightarrow\hept{\begin{cases}\left(153-3\right)⋮x\\150⋮x\left(1\right)\end{cases}}\)
\(\text{123 chia x dư 23 }\Rightarrow\hept{\begin{cases}\left(123-23\right)⋮x\\100⋮x\left(2\right)\end{cases}}\)
\(\text{Từ ( 1 ( và ( 2 ) suy ra }x\inƯC\left(150,100\right)\)
\(\text{Ta có : }\hept{\begin{cases}100=2^2.5^2\\150=2.3.5^2\end{cases}\Rightarrow\left(100,150\right)=2.5^2=50}\)
\(\Rightarrow x\inƯ\left(50\right)=\left\{1;2;5;10;25;50\right\}\)
\(\text{Mà }x>23\Rightarrow x\in\left\{25;50\right\}\)
\(153\text{ : }x\left(\text{ dư }3\right)\Rightarrow\text{ }\left(153-3\right)\text{ }⋮\text{ }x\text{ }\Rightarrow\text{ }150\text{ }⋮\text{ }x\) \(\Leftrightarrow\text{ }x\inƯ\left(150\right)\)
\(123\text{ }⋮\text{ }x\left(\text{ dư }23\right)\text{ }\Rightarrow\text{ }\left(123-23\right)\text{ }⋮\text{ }x\text{ }\Rightarrow\text{ }100\text{ }⋮\text{ }x\) \(\Leftrightarrow\text{ }x\inƯ\left(100\right)\)
\(\hept{\begin{cases}150\text{ }⋮\text{ }x\\100\text{ }⋮\text{ }x\end{cases}}\text{ }\Rightarrow\text{ }\hept{\begin{cases}x\inƯ\left(150\right)\\x\inƯ\left(100\right)\end{cases}}\Rightarrow\text{ }\text{ }x\inƯC\left(150\text{ },\text{ }100\right)\)
\(\text{Ta có : }\)
\(150=2\cdot3\cdot5^2\) \(100=2^2\cdot5^2\)
\(\Rightarrow\text{ ƯCLN}\left(150\text{ , }100\right)=2\cdot5^2=50\)
\(\text{ƯC}\left(150\text{ , }100\right)=Ư\left(50\right)=\left\{1\text{ ; }2\text{ ; }5\text{ ; }10\text{ ; }25\text{ ; }50\right\}\)
\(\text{Mà }\hept{\begin{cases}x>3\\x>23\end{cases}}\Rightarrow\text{ }x\in\left\{25\text{ ; }50\right\}\)
\(\Rightarrow\text{ }\hept{\begin{cases}x=28\\x=53\end{cases}}\)
\(\text{Nguyễn Châu Tuấn Kiệt bạn làm thiếu một bước rồi đó ! }\)
\(\Rightarrow\text{ }\hept{\begin{cases}x=28\\x=53\end{cases}}\)
\(\text{Chúc bạn học tốt !}\)
