Panik

ickplant@lemmy.world to Lemmy Shitpost@lemmy.world – 1244 points –
144

Also, any number whose digits sum to a multiple of 3 is divisible by 3. For 51, 5+1=6, and 6 is a multiple of 3, so 51 can be cleanly divided by 3.

I'd forgotten this trick. It works for large numbers too.

122,300,223÷3 = 40,766, 741

1+2+2+3+2+2+3 = 15

threw up and died while reading this

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'll get you NEXT time logicbomb!

Same with 9. There are rules for every number at least through 13 that I once knew...

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.

7 is double the last number and subtract from the rest

749 (easily divisible by 7 but for example sake)

9*2=18

74-18=56

6*2=12

5-12= -7, or if you recognize 56 is 7*8...


I'll do another, random 6 digit number appear!

59271

1*2=2

5927-2=5925

5*2=10

592-10=582

2*2=4

58-4=54, or not divisible

I guess for this to work you should at least know the first 10 times tables...

Another way to tell if 59271 is divisible by 7 is to divide it by 7. It will take about the same amount of time as the trick you're presenting, and then you'll already have the result.

But at least I seems like you could do that trick in your head

If you have no interest in the result of the division, then you can also do the division in your head, without retaining the result, with about the same effort.

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I'm sure every digit has rules to figure it out if you get technical enough.

I looked up a rule for 7, and it seems like it would take about the same amount of time as actually dividing the number by 7.

Meanwhile, it looks like the rule for 8 is to see if the last 3 digits are divisible by 8, which seems like a real time save for big numbers.

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11 is alternating sum
So, first digit minus second plus third minus fourth...
And then check if that is divisible by 11.

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And since both 3 and 17 are prime numbers, that makes 51 a semiprime number

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

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51 = 3*17

3*17 = 17 + 17 + 17

17 + 17 + 17 = (10+7) + (10+7) + (10+7)

(10+7) + (10+7) + (10+7) = 30 + 21

30 + 21 = 51

yup, math checks out

I think you skipped a step:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

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.

You miss a couple os steps too.

First, lets define the axioms, we're using Peano's for this exercise.

Axiom 1: 0 is a natural number.

Jump to axiom 6, define the succession function s(n) where s(n) = 0 is false, and for brevity s(0) = 1, s(s(0)) = 2 and so on...

51 = 3*17

3*17 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3

3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1)

(2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) + (2+1) = 34 + 17

34 + 17 = 51

👌

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.

Our plan to find the witch has worked, boys! Get her!

For divisibility by 13, take the last number, multiply by 4 and add to the rest.

For divisibility by 17, take the last number, multiply by 5 and subtract from the rest.

For divisibility by 19, take the last number, multiply by 2 and add to the rest.

In fact, you can adapt the method to check for divisibility by any prime number k.

Quick check for divisibility: subtract 7 from it. If the new number is divisible by 7, then the original number is too

okay I understand that this works, but is there a mathematical proof for this?

There is a mathematical algorithm that proves this works in all cases. However this rule is not actually all that impressive as it appears at first glance! The number of operations (comparisons/subtractions/multiplications) you need to do is equivalent to just long-dividing the number by 7.

Consider: each operation of the rule removes one digit from the end. But you could just as easily apply the rule like "If the first digit is >=7, subtract 7 from it. Else, subtract the biggest multiple of 7 that will fit from the first two digits." To skip multiplying, you can use the following jump table: if the first digit is 6, subtract 54 from the first 2 digits, if 5 subtract 49, if 4: 35, if 3: 28, if 2: 14, if 1: 07. That will also remove one digit from the front! But now you are just doing long division.

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

27943 - 7*1000 = 20943

20943 -7*3*1000 = 20943 - 21000 = -57

-57 is not divisible by 7 therefore 27943 is not divisible by 7.

The other posters algorithm was better, but I was exaggerating - ultimately my point is you have to math it out

Any number where the individual digits add up to a number divisible by '3' is divisible by 3.

51 = 5+1 = 6, which is divisible by three.

Try it, you'll see it always works.

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.

double it and add it to subtract it from what’s left

14: 1 + 8 = 7. Not db7

You clearly mean:

14: 1 + 8 = 9 (not db 7)

Someone else in this thread correctly stated:

"Chop of last digit, double it and subtract from what is left"

14: 1 - 8 = -7. (dB 7!)

Math is awesome, I didn't know this trick!

One of the reasons why I love the number 3. There are other neat digit sum tricks, see for example for the numbers 1 to 30 here: https://en.m.wikipedia.org/wiki/Divisibility_rule

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.

My experience of maths in high school was being taught a trick or method to solve a really specific type of problem every week. Sometimes the method would build off something we'd learnt the previous week.

The whole thing was bottom-up learning where you get given piecemeal nuggets of information but never see the big picture. They completely lost me at around the age of 15. I eventually came back to maths later in life after studying formal logic in my philosophy undergrad degree.

I guess I was one of the lucky few who learned this in elementary school. And later again.

I knew that worked with 9. Hmm, does it work with 6?

Doesn’t look like it.

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.

wait till she finds out that 0.99999... 9's to infinity is the same as 1

Lmao how about ...99999 = -1?

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.

Yes, you're right this doesn't work for real numbers.

It does however work for 10-adic numbers which are not real numbers. They're part of a different number system where this is allowed.

You can also prove it a different way if you allow the use of the formula for finding the limit of the sum of a geometric series on a non-convergent series.

Sum(ar^n, n=0, inf) = a/(1-r)

So,

…999999

= 9 + 90 + 900 + 9000…

= 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3…

= Sum(9x10^n, n=0, inf)

= 9/(1-10)

= -1

But why would you allow it?

Because you could argue that the series converges to …999999 in some sense

I love how every reply has like the opposite energy to the meme. I also find math to be generally awesome.

Math is hard, so I'm just going to assume that's true and move on with my day.

When you start playing modded minecraft you get really good at multiplying and dividing by 144

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.

Upon closer inspection, yeah. 51 = 17 × 3

= (10 + 7) × 3

= (10 × 3) + (7 × 3)

= 30 + 21 = 51

EDIT: Brackets added.

= 10 × 3 + 7 × 3

Careful, that's how you get a Facebook thread with people claiming 51 = 111... /s

Would it be better to add brackets? I think I'm gonna edit to add brackets.

EDIT: I edited to add brackets.

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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?

17 is a prime number. 3 is a prime number.

all numbers can be factored down to primes.

19 is a prime number.

19*3=57. is that one gross too?

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.

This is the only one kind of math that professional darts players will dominate.

I actually really like this. 17 is three less than 20, 20x3 is 60, 3x3 is 9, 51 is 60-9. It just feels nice how it all fits together.

Technically, isn't everything divisible by any number? You just get remainders and/or fractions in the result?

I mean, I still didn't want to know this, but....

The definition for "divisible" is being able to be divided without a remainder.

By definition to be divisible by a number you have to a have a whole number with no remainder as an answer

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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..

But it's in a British accent, it automatically makes you smarter!

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Obligatory

Piped is a privacy-respecting open-source alternative frontend to YouTube.

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I wasn't that surprised to be honest... but than again, I'm divergent 🤷.

Same same. I was like "its 3x20 minus 3x3, 60 minus 9...?"

Yeah, I would be like 😲 for 101, but 51... yeah, not that surpised.

What the fuck does divergent mean? Are you divisible by 17 or not?

lol 🤣🤣🤣 i might be, depends how you look at things 🤣