this post was submitted on 22 Oct 2023
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Take the last digit of the number, double it and subtract it from the rest. If that new number is divisible by 7, the original one is as well. For your example:
2794 - 6 = 2788
I know 2800 is divisible by seven, so 2788 is not. Thus 27943 is not divisible by 7.
Quick maff shows that neither subtracting 3 or adding 4 will make the original number divisible by 7.
Quick check for divisibility: subtract 7 from it. If the new number is divisible by 7, then the original number is too
But what about 14, 21 and 28?
14 - 4*2 = 6, not divisible by 7
21 - 1*2 = 19, not divisible by 7
28 - 8*2 = 12, not divisible by 7
Or did I misunderstand the algorithm?
It goes like this
create 2 distinct numbers by isolating the last digit from the other. For example, 154 becomes 15 and 4.
double the number derived from the last digit. So, the four becomes 8.
subtract from the number derived from the preceeding digits. 15 - 8.
the resulting number is 7. Seven is divisible by 7, so we know 154 is divisible by 7.
Yeah you got it wrong, it's
1 - 4*2 = -7
2 - 1*2 = 0
2 - 8*2 = -14