  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  Solution

The correct option is D all of theseLet 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 7so in 111111$$11111-2=11109$$which is divisible by 7so 111111 is also divisible by 7A 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 11A number is divisible by 13 if add four times the last digit to the remaining leading truncated number and  the result is divisible by 13in 111111$$11111+4=11115$$which is divisible by 13so 111111 is also divisible by 13Hence any number like$$555555=5(111111)$$is also divisible by 7,11,13 So option D is answerMathematics

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