\(36:x\)dư 6\(\Rightarrow36-6⋮x\Rightarrow30⋮x\left(x>6\right)\)
\(46:x\) dư 1 \(\Rightarrow46-1⋮x\Rightarrow45⋮x\left(x>1\right)\)
\(\Rightarrow x>6;x\inƯC\left(30;45\right)\)
\(30=2.3.5\)
\(45=3^2.5\)
\(UCLN\left(30;45\right)=3.5=15\)
\(UC\left(30;45\right)=Ư\left(15\right)\)
\(Ư\left(15\right)=\left\{\pm1;\pm3;\pm5;\pm15\right\}\)
Mà chỉ có: \(15>6\)
\(x=15\)