this post was submitted on 22 Oct 2023
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This is why I love the number 7. It's the first real prime number. All the others are "first"...1?2?3?5? No, those aren't prime numbers, they're "first" in a long line of not-prime numbers.
Then you get to 7. Is 27943 divisible by 7? If you take away 3 is it? If you add 4 is?
I have no clue, give me 10 minutes or a calculator is the only answer
That's what a real prime number is.
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. Adding 1 or subtracting 6 will tho.
~~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?~~
EDIT: I didn't realize that you remove the last digit when subtracting, got corrected in the replies.
Yeah you got it wrong, it's
1 - 4*2 = -7
2 - 1*2 = 0
2 - 8*2 = -14