Divisibility Rules for 11
If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
In order to check whether a number like 2143 is divisible by 11, below is the following procedure.
- Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here 24 and 13 are two groups.
- Take the sum of the digits of each group i.e. 2+4=6 and 1+3= 4
- Now find the difference of the sums; 6-4=2
- If the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is the difference which is not divisible by 11.
- Therefore, 2143 is not divisible by 11.
Solution
Given digits: 0,1,2,4,5,7,9
Sum of the given digit is 0+1+2+5+7+9 = 24
Let the digits be abcdef
The numbers abcdef is divisible by 11 if
For a number to be divisible by 11 , difference of sum of alternate digits of the number should be of the form
|(a+c+e )-(b+d+f)is a multiple of 11
a+c+e=b+d+f=12
Case 1: {a,c,e}={7,5,0}
{b,d,f}={9,2,1}
So, 2 x 2! x 3! = 24
Case 2: {a,c,e}={9 , 2, 1}
{b,d,f}={7, 5, 0}
So, 3! x 3! = 36
Total = 24 + 36 = 60
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Maths