Numbers which get reduced by 57 times on deleting the leading digit.

Question

If the leading digit of a positive integer is deleted, the number gets reduced by 57 times. Find all such numbers.

Answer 1

$$57\cdot n=10^r m+ n\iff56n=10^r m$$

$\iff8n=\dfrac{10^rm}7\implies 7\mid m, m=7q$(say)

As $0<m<10, m=7$

$\implies8n=10^r\implies r\ge3, n=5^r2^{r-3}$