Divisibility test by 7 - Extended

After my earlier blog on divisibility by 7, I was checking the web for some more interesting ways to do the same check. I came across two more ways from this site. I'm presenting the way to do it with my own example here.

Method 3 : (for earlier methods refer here)

Starting from right to left, multiply with the digits with the numbers 1, 3, 2, 6, 4, 5 and do repeated addition.

Let us take the number 778701 as an example.

We get 1 * 1 + 0 * 3 + 7 * 2 + 8 * 6 + 7 * 4 + 7 * 5
= 1 + 0 + 14 + 48 + 28 + 35
= 126

Clearly, 126 is divisible by 7 and hence 778701 is divisible by 7. Try the test for your sample number and post your comments..

Method 4 : Double and subtract.

Take the unit digit of the number, double it and subtract the result from other numbers. Continue doing so until you get a single digit number. If the single digit is a 0 or 7 then the original number is divisible by 7.

Let us take the number 778701 as an example.

77870 - (2 * 1) = 77868
7786 - (2 * 8) = 7770
777 - ( 2 * 0) = 777
77 - (2 * 7) = 63
6 - (2 *3) = 0

Hence, the number is divisible by 7.

However, if you compare the methods with the previous post you will find that the old one is still good.

In this case, it will be the difference of 778 and 701 which is 77 and is divisible by 7. Quick, ain't ?