Gọi số cần tìm là \(\overline{abc}\) (a,b,c∈N;\(0< a\le9;0\le b;c\le9\))
Theo bài ra, ta có:
\(\left\{{}\begin{matrix}\left(\overline{abc}-4\right)⋮25\\\left(\overline{abc}-7\right)⋮28\\\left(\overline{abc}-14\right)⋮35\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left(\overline{abc}+21\right)⋮25\\\left(\overline{abc}+21\right)⋮28\\\left(\overline{abc}+21\right)⋮35\end{matrix}\right.\)
\(\Rightarrow\left(\overline{abc}+21\right)⋮700\)
\(\Rightarrow\overline{abc}+21=700\Rightarrow\overline{abc}=679\)
Vậy số cần tìm là 679
