Yet another Divisibility by 7 !

Much about checking if a number is divisible by 7 is done here and here. And it is not over yet! Here is one more approach that tells you if a number is divisible by 7 or not.

The approach goes like this. Take the first two digits of the number from the left. Multiply the leftmost of that number by 3 and add it to the second digit. Replace the first two digits with this result. Continue the same process until you get a number which you can deduce for sure that it is divisible by 7. This can be better understood by the following example. Take the number

857864.

The first two digits are '85'. Multiply 8 by 3 and add it to 5. This gives 29. So the number is changed as

297864

Repeating the same process, we get

157864
87864
31864
10864
3864
1764
1064
364
154
84

And of course, 84 is divisible by 7. Hence the number 857864 is divisible by 7. Cool.. So, now we have four approaches to find out if a number is divisible by 7 or not. Make sure you check out the approaches listed here and here.

Did you notice something in this approach? How does this work? Are you able to see a pattern in this execution?

In a different post of mine, I will explain how this approach works and can be generalized.