Question

There is one number which is formed by writing one digit 6 times, such number is always divisible by:
(e.g., 0.111111,0.444444 etc)

• A. 7
• B. 11
• C. 13
• D. all of these

Answer 1

The correct option is D all of these

Let the number is $111111$
A number is divisible by 7 if we double the last digit and subtract it from the remaining leading truncated number and the result is divisible by 7
so in 111111$11111-2=11109$which is divisible by 7
so 111111 is also divisible by 7
A number is divisible by 11 if we subtract the sum of odd digit number with sum of even digit number, we get 0 or any number that is divisible by 11
In 111111 $(1+1+1)-(1+1+1)=0$
so 111111 is divisible by 11
A number is divisible by 13 if add four times the last digit to the remaining leading truncated number and the result is divisible by 13
in 111111$11111+4=11115$which is divisible by 13
so 111111 is also divisible by 13
Hence any number like$555555=5\left(111111\right)$
is also divisible by 7,11,13
So option D is answer