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
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.
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 721 - 1*2 = 19, not divisible by 728 - 8*2 = 12, not divisible by 7Or did I misunderstand the algorithm?EDIT: I didn’t realize that you remove the last digit when subtracting, got corrected in the replies.
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.
Quick check for divisibility: subtract 7 from it. If the new number is divisible by 7, then the original number is too
27943 - 7*1000 = 20943
20943 -7*3*1000 = 20943 - 21000 = -57
-57 is not divisible by 7 therefore 27943 is not divisible by 7.