The neat part is that if you add the numbers together and they're still too large to tell, you can do it again. In your example, you get 15. If you do it again, you get 6, which isn't the best example because 15 is pretty obvious, but it works.
Fuck you and take an upvote for coming here to state what I was going to when I immediately summed 5+1 to 6 and felt clever thinking "well I do know it's not prime and divisible by 3"
Shakes fist
I only know rules for 2 (even number), 3 (digits sum to 3), 4 (last two digits are divisible by 4), 5 (ends in 5 or 0), 6 (if it satisfies the rules for both 3 and 2), 9 (digits sum to 9), and 10 (ends in 0).
I don't know of one for 7, 8 or 13. 11 has a limited goofy one that involves seeing if the outer digits sum to the inner digits. 12 is divisible by both 3 and 4, so like 6, it has to satisfy both of those rules.
Which is why it feels kind of prime, imho. I don't know if other people get this, but I get a sense of which two-digit numbers are prime probably because of how often they show up in times tables and other maths operations.
3*17 isn't a common operation though and doesn't show up in tables like that, so people probably aren't generally familiar with it.
Does this also work the other way round, i.e. do all multiples of three have digits that sum to a multiple of 3?
All the ones I've checked so far do, but is it proven?
Indeed, an integer is divisible by 3 if and only if the sum of its digits is divisible by 3.
For proof, take the polynomial representation of an integer n = a_0 * 10^k + a_1 * 10^{k-1} + ... + a_k * 1. Note that 10 mod 3 = 1, which means that 10^i mod 3 = (10 mod 3)^i = 1. This makes all powers of 10 = 1 and you're left with n = a_0 + a_1 + ... + a_k. Thus, n is divisible by 3 iff a_0 + a_1 + ... + a_k is. Also note that iff answers your question then; all multiples of 3 have to, by definition, have digits whose sum is a multiple of 3
Edit: Ohhhh, math by tens, I totally missed it. In that case, my mind wants to break it down to (10 * 5) + 1, and I'd still totally miss 17 as a possible factor.
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.
There are tricks like that for a lot of numbers. For 7, chop off the last digit, double it and add it to what's left. Repeat as required. If the result is divisible by 7 then the original number was. eg: 356 -> 35+12=47 not db7. 357 =>35+14 both db7 so we don't even need to do the add.
They didn't teach stuff like this in school, which is silly. This is the kind of thing that a kid would eat up. It's like they wanted to make sure people hated math.
Technically it does work for 6, more literally, still aiming for 3, not 6. That's half of it, if the starting number is even and divisible by 3 then it is also divisible by 6.
This one has always bothered me a bit because ....999999 is the same as infinity, so when you're "proving" this, you're doing math using infinity as a real number which we all know it's not.
I used to do this thing where I would figure out if a number was prime or not and it kept me sane. Realizing this isn't, may have just caused my whole world to fall apart.
weird how ppl are getting all excited over this. weirder all the random math facts on the comments. and everyone checking with long math as if it might not be lol. I guess I'll throw a few math facts in?
What's weird is that 17 feels like a small enough number where it seems like we should know intuitively what its multiples are. And it feels like by this point in our lives we should at least know all numbers up to 100 or so that are composite vs prime. But yeah it's actually not that weird when you consider that the multiplication table usually stops at 12. And also that we really don't get that much exercise in multiplication in daily life.
WTF, we are making videos from text posts now ? It feels so weird...
Instead of reading a post in 10s, I get to wait 35s for the video to unfold the text discussion, and youtube gets to puts ads on top of it, what a time to be alive..