Gọi số đó là \(\overline{abc}\left(a\ne0;0\le a,b,c< 10\right)\)
Ta có \(\overline{abc}=5abc\left(a,b,c\ne0\right)\)
Vì \(5abc⋮5\) nên \(\overline{abc}⋮5\)
Do đó \(c=5\left(c\ne0\right)\)
\(\overline{abc}=5abc\Rightarrow\overline{ab5}=25ab\\ \Rightarrow100a+10b+5=25ab\\ \Rightarrow20a+2b+1=5ab\)
Vì \(5ab⋮5;20a⋮5\) nên \(2b+1⋮5\)
\(\Rightarrow b\in\left\{2;7\right\}\left(0\le b< 10\right)\)
Với \(b=2\Rightarrow\overline{a25}=50a\)
\(\Rightarrow100a+25=50a\\ \Rightarrow50a=-25\\ \Rightarrow a=-\dfrac{1}{2}\left(vô.lí\right)\)
Với \(b=7\Rightarrow\overline{a75}=5a\cdot5\cdot7\)
\(\Rightarrow100a+75=175a\\ \Rightarrow75a=75\Rightarrow a=1\left(tm\right)\)
Vậy \(\overline{abc}=175\)
