New Formula For Divisibility Of 8 Discovered By Me

We can find whether a number is divisible by 8 or not by following steps:

1# first multiply the no. Leaving ones digit by 2 or leaving the last 2 digit by 4 ( leaving last n digits by 2^n)and add the leaves no. , if the result is divisible by 8 the original no. Is divisible by 8 , to check whether the resulting no. Is divisible by 8 or not repeat the process.

Ex. Let original no. Be 34512 now leaving last digit , 3451x 2 +2( 1 digit is leave(2^n))

3451×2 +2= 6904 , 690×2+4= 1384, 138×2+4= 280, 28×2+0=56is divisible by 8 so 34512 is divisible by 8

Note by Hemant Kaushik
2 weeks ago

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Can you use LaTeX and paragraphs, please?

Because it's big and bulky...

Yajat Shamji - 2 weeks ago

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I'll rephrase it in a more straightforward way:

810a+b82a+b8|10a + b \rightarrow 8|2a + b for positive integers aa and bb. The "new divisibility rule" takes advantage of that, and iterates using that.

I personally don't see the point in applying this, the conventional method is much faster.

Elijah L - 2 weeks ago

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Take an ex. 6948, 69×4+48= 324, 3×4+24= 36 not divisible by 8 so 6948 is not divisible by 8 . Isn't this easy

Hemant Kaushik - 2 weeks ago

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@Hemant Kaushik Sure, but the conventional rule is to take the last 33 digits of the number and see if that is divisible by 88. That way, I only need to do 11 total operation, as compared to your 22 for 69486948. I don't see a point in using a less efficient method to test for the divisibility rule of 88.

Elijah L - 2 weeks ago

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Yeah, but my rule also describes the conventional rule although the conventional rule is a part or simplification of my rule as , let we leave last three digits than the no. Left we have to multiply by 8 as of 2^3(formula for n digits leaved is 2^n)and add the leaves no. , Now if the leaved no. ( The last three digits of original no. ) Is divisible by 8 then adding the multiplied no will be divisible by 8 that why we need just last three digits , it also describes how last two digits are taken in case of 4. It is not just a Divisibility rule for 8 , it is for all powers of 2(2^n) . Seems like it has gone very lengthy , sorry as I am not a good explainer .

Hemant Kaushik - 2 weeks ago

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