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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 :


Solution

Let the no. be $$'a aa aaa'= N $$
$$(1\leq a\leq 9)$$ 
$$N=a[111111]$$
As $$'111111'$$ is divisible by $$7,11$$ and $$13$$ 
$$\therefore $$ $$'N'$$ is divisible by $$7,11$$ and $$13$$.

Mathematics

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