Witchcraft! Burn them!
Comment on Panik
logicbomb@lemmy.world 8 months ago
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.
paddirn@lemmy.world 8 months ago
Steeve@lemmy.ca 8 months ago
She turned me into a newt!
directive2385@sh.itjust.works 8 months ago
…I got better
MechanicalJester@lemm.ee 8 months ago
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!
Dagwood222@lemm.ee 8 months ago
Posted the same info. Silly me
beckerist@lemmy.world 8 months ago
Same with 9. There are rules for every number at least through 13 that I once knew…
logicbomb@lemmy.world 8 months ago
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.
beckerist@lemmy.world 8 months ago
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…
logicbomb@lemmy.world 8 months ago
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.
octoperson@sh.itjust.works 8 months ago
11 is alternating sum
So, first digit minus second plus third minus fourth…
And then check if that is divisible by 11.Frozengyro@lemmy.world 8 months ago
I’m sure every digit has rules to figure it out if you get technical enough.
logicbomb@lemmy.world 8 months ago
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.
kibiz0r@midwest.social 8 months ago
What does the proof for this look like?
Ulvain@sh.itjust.works 8 months ago
90°
Iron_Lynx@lemmy.world 8 months ago
And since both 3 and 17 are prime numbers, that makes 51 semiprime.
KevonLooney@lemm.ee 8 months ago
Which is not really rare under 100.
Excrubulent@slrpnk.net 8 months ago
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.
WhiskyTangoFoxtrot@lemmy.world 8 months ago
Do do do, do do do do.
Sadbutdru@sopuli.xyz 8 months ago
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?
goddard_guryon@sopuli.xyz 8 months ago
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
Sadbutdru@sopuli.xyz 8 months ago
Thank you for this detailed response 🙏
GladiusB@lemmy.world 8 months ago
Username checks out
fleabomber@lemm.ee 8 months ago
Show off
Black_Gulaman@lemmy.dbzer0.com 8 months ago
Til thanks
flambonkscious@sh.itjust.works 8 months ago
Damn, logicbomb indeed!
Fades@lemmy.world 8 months ago
Oh, neat trick!
Vorticity@lemmy.world 8 months ago
I’d forgotten this trick. It works for large numbers too. 122,300,223÷3=4,07
FlexibleToast@lemmy.world 8 months ago
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.
starman2112@sh.itjust.works 8 months ago
But how do I prove it for 6
GladiusB@lemmy.world 8 months ago
Get 6 apples. Duh.
Rodeo@lemmy.ca 8 months ago
There is a mathematical proof that 1 + 1 = 2 so surely you could make a proof for 6 ÷ 3 = 2
postmateDumbass@lemmy.world 8 months ago
Prove it for 2, then un-distribute.