Question

if 604_6 divisible by 11 , then the integer in the blank space is =

Answer 1

Divisibility rule of 11:
The difference between the sum of numbers in odd places and the sum of numbers in even places is zero or 11
Solution:
Let the missing number be 'x'
The numbers in odd places are 6,4,6
The numbers in even places are 0,x
The sum of numbers in odd places is 16
The sum of numbers in even places is x
x can between 0 to 9
The difference should be 11
i.e 16-x = 11
=> x = 5
The number is 60456
Check:
 11 ) 60456 ( 5496
     - 55
---------------
         54
       - 44
----------------
         105
         - 99
---------------
            66
          - 66
-----------------
             0
-----------------

Answer 2

Solution :-

Divisibility of 11 -

If a number is divisible by 11, if the difference between the sum of the digits at the odd places and the sum of the digits at the even places is either 0 or 11.

604_6 ÷ 11

Let the number at the blank space be 'x' 

Sum of the digits at odd places = 6 + 4 + 6 = 16

Sum of the digits at even places = 0 + x

The digit at the blank space must be from 0 to 9.

⇒ Difference must be either 11 or 0.

16 - (0 + x) = 0                           or            16 - (0 + x) = 11
          
16 - x = 0                                                   16 - x = 11

x = 16, which is not possible.                     x = 16 - 11

                                                                  x = 5

So, the number is 60456

⇒ 60456  ÷ 11

Quotient = 5496

Remainder - 0