Mathematics - Permutation & Combination Question with Solution | TestHub

$N=a_n{a}_{n-1}{a}_{n-2}\dots a_2{a}_1{a}_0$$\begin{array}{rl}& \frac{N}{57}=a_{n-1}\cdot a_{n-2}\dots a_2{a}_1{a}_0\\ & a_{n}10^n=56\left(a_0+10a_1+100a_2\dots +10^{n-1}{a}_{n-1}\right)\\ & \Rightarrow 56\text{ divides }{a}_{n}10^n\\ & \Rightarrow a_n=7,n\ge 3\\ & \Rightarrow 5^3=a_0+10a_1+10^2{a}_2\\ & \Rightarrow \text{ The required }\mathrm{N}=7125\text{ (or) }71250\text{ (or) }712500\text{ etc }\\ & \Rightarrow \text{ sum of digits }=15\end{array}$