Question

what is the sum of the digits of the smallest positive integer which is divisible by 99 and has all of its digit equal to 2

Answer 1

The number 99 can be written as 9*11  

So the number we need must be divisible by 9 and 11.  

For finding the number lets take the number be, abcdef……….. which is divisible by 9 and 11

 If we have to find  abcdef………. Divisible by 9 then (a+b+c+d+e+f………….) be a multiple of 9.  

But this case a=b=c=d=e=f……………=2  

So this number must contain 2,4,6,8,10,12,14,…….  

That is any even number of digit  

Therefore the smallest number must have 18 digit  

That is 222222222222222222  

And the sum of the digit  is 18*2=36