Divisibility rules - 7 and 11

Quote : Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics.                                                                                  --Anon

How do you check a number is divisible by 7?

Pull out unit digit number, double and subtract the remaining number. Repeat this process till you get significant small number.

Let me take one example
Ex : 12896
step 1: pull out unit digit number i.e. 6
           double it i.e. 12
       2: 1289 - 12 = 1277
Repeat above process.
       127 - 2x7 = 127 - 14 = 113
 113 is not divisible by 7. So 12896 is not divisible by 7.

How do you check a number is divisible by 11?

This can be done by addition and subtraction. Add all odd place digits and even place numbers. If the difference of these two is 0 or divisible by 11, then the number is divisible by 11.

Let me take an example
Ex : 123454321
sum of odd place digits = 1 + 3 + 5 + 3 + 1 = 13
sum of even place digits= 2 + 4 + 4 + 2 = 12
difference of above sums = 13 - 12 = 1

It is not 0 or divisible by 11.
So 123454321 not divisible by 11.

So far from 2 to 11 divisibility rules covered.