Question

There is one number which is formed by writing one digit 6 times
(e.g. 111111, 444444 etc.). Such a number is always divisible by :

Answer 1

Let the no. be ${}^{\prime }aaaaa{a}^{\prime }=N$

$(1\le a\le 9)$

$N=a\left[111111\right]$

As ${}^{\prime }{111111}^{\prime }$ is divisible by $7,11$ and $13$

$\therefore$ ${}^{\prime }{N}^{\prime }$ is divisible by $7,11$ and $13$.