Finally, a trick for determining divisibility by 37! More math chats: ua-cam.com/play/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO.html Join Wrath of Math to get exclusive videos, lecture notes, and more: ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
Once to challenge myself I tryed to purely in my head find all the prime numbers going up to 1000... I eventually got there; after cheating to remember where I left off on the list. My point being is that it can be hard even with tricks to still do these things in your head. One trick I did find that was somewhat strange was that 21X21 and 12X12 have reflective answers; OK its been years so maybe its not specifically 12 but when going through double digits you will come across some that do work that way. Thought of as a kid in middle school while bored and having paper to do simple math repeatedly. No clue if it has a term already or not.
After finishing with the 999's, if you are left with a three-digit number, you can then cast out 111's until you get to a two-digit number. (Or a one-digit number, or a number between 100 and 110, but let's not get picky.) Just subtract one from each digit at a time. 1⁻¹4⁻¹8⁻¹ -> 037. (⁻¹ is not an exponent here.)
Just subtract the highest multiple of 111 that’s less than N, pretty easy to eyeball that. 111, 222, 333,…888, that leaves you with a number less than 111. Any number less than 111 (3*37) is divisible by 37 only if it’s 0, 37, or 74. If you want the remainder, subtract the largest of those from the your result and you get the remainder mod 37.
I think the only reason why I was recommended thiz is because I sometimes watch videos on niche math theorems and happened to be watching Nintendo related content earlier. How is Nintendo relevant? Half the way through, I realized Pikmin music was playing.
Fun fact: the process of casting out nines, when iterated on a number (as demonstrated in the video), is essentially the same process as finding the digital root. You add up every digit, take the result, then repeat (iterate) if the result has multiple digits, until you end up with a single digit, which is your digital root. The only thing different from casting out nines is that unless you start with 0, a number divisible by 9 will have the digital root of 9 (in casting out nines, the result would be 0).
I actually decided to make this video as an offshoot of working on a video about digital roots. Will come back to the digital root video at some point, but figured casting out 9s deserved its own video!
I was thinking exactly the same! I believe that by only adding every digit we spare the other operation, like cheking for 9's (which by itself is a complex operation which involves adding + comparison + substracting/casting out). Thus, with only a simple operation (adding) we can get a faster result with less resources (CPU power). However, I guess this is usefull when trying to optimize computer code but for other purposes, like math studies, going the extra mile might be worting.
This is why i decided to go into engineering. Math just feels like magic sometimes, and yet time and time again, it proves to be more useful than we even considered. For example, black holes were originally theorized in 1796 (by Laplace, whoda thought?), were modeled mathematically in 1916 by Schwarzschild, but they weren't widely accepted as real until the 1970s, and now we have pictures of them! Math is sorcery
Divisible by 10 to result into an integer. Everything is divisible by anything. You just won't always get whole numbers. That's not an error. That's just indicating a natural log.
Could you make a video proving this? I know it has a name, but I can’t think of what it is called right now. Basically can you make a video proving that n squared is always one greater than (n-1)(n+1)? For example, 2^2 is 1 greater than (2-1)(2+1). 4 is one more than 3.
my brain does weird things sometimes. finds the remainders of random numbers after dividing by specifically factors of 999, like 37 and 27. quite cool to actually see a video talking about this weird obsession i have
in other words. 1) split the number into groups of 3 digits. 2) sum all the numbers from step 1. 3) cast out nines. 4) remember all numbers less than 999 that can be divided by 37. 😅 unless... you remember that 37*3=111 so we can further reduce the number taking 1 from every position. for example: 148-111=37 it's still a pita for some numbers but it can help to further reduce how many multiples of 37 we need to remember.
I've only ever heard of this casting out 9s trick being used to test if the number is divisible by 3 or 9. If it is divisible by 9, casting out 9s gives a zero. If there's anything left over after casting out 9s, it's not divisible by 9 and what is left over is the remainder after dividing by 9. If that remainder is 3 or 6, the number is divisible by 3. I've never heard of it being used as a "check your answer" trick or a divisibility by 11 or 37 trick. The one trick I have heard of for divisibility by 11 is to take the sum of the digits in the odd places and subtract the sum of the digits in the even places and if that difference is divisible by 11, the original number is too.
! like the Hitch Hikes Guide to the Galaxy number of 42. How long would it take to double your money with interest? At 6% its 7 years multiply years by interest and the answer must be 42.
You keep making mistakes in your casting out of nines. I mean, technically they end up working out but it is a poor demonstration because you keep missing other nights you could have cast out.
2:16 I found the sum mentally, but that addition CAN be done on the calculator. We can see that the solution will be ten digits in length, and the calculator simply truncated the number and cut off the last digit. We can see that the units digits, when added together, give us a unit digit of 1. So we tack that 1 onto the end of the solution shown in the display.
This is kinda off topic, but is the music in the background of the video an arrangement of Xenoblade Chronicles OST - Valak Mountain (Night). It sounds pretty much the same except for the music in this video has less instruments so its a more gentle arrangement of that song. If I am wrong, does anyone know what the song playing is?
I tried this trick with the number of ppl who have clicked on this video and added those three digit numbers together (00X + XXX) . I got 635. 000 + 635 is 635. I still don't know if clicks on video was divisible by 37. Then I tried subtracting 100 * 37 from the number and try the trick from there. I got 933. Just as insightful as the last try, wtf! But after like 10 seconds of thought, I realized that 933 is pretty close to 999, so adding 2 * 37 added to 933 and compare those numbers should give you the mod remainder. So 1007. 8 should be the remainder. But it took me minutes to figure out so I don't think it is a nice trick. You can reverse engineer my calculation more easily to figure out the view count I saw.
@justsaadunoyeah1234 bruuhhh, anyways, the reason why 23 is my favorite number is because i like the way it looks, My birthday being December 23 and all about the Birthday Paradox
So p is some prime number and n is p-1, but I am not sure what you’re trying to “find”. The “n” itself seems to be part of the fraction. What does that fraction equates to?
Why did you say “casted”? The past tense of “cast” is “cast, just as the past tenses of “put” and “hit” are (surprise!) “put”and “hit.” Will your next video say that you “putted” down the answer and it “hitted” the mark accurately?
i know the past tense of cast is cast, but it doesn't sound like past tense, by saying 'casted' it is clearly past tense, even if not technically correct, so the listener knows i am referring to something we already did, not something we must now do. yes my next video will say that
These are good and valuable tricks, and well presented. But at about the 2:20 mark, the lecturer dismisses as “a tall tale“ the existence of calculators that can handle more than eight digits, and that’s ridiculous! That little T.I. calculator he’s using was left in the dust long ago. My iPhone is an SE model quite a few years old, and its scientific calculator can handle numbers of up to 16 digits. Divisibility tests for several different numbers are mentioned and explained in this talk, which is all well and good. But it should be noted that these numbers are in no way unique for having divisibility tests; in fact, it is not difficult to construct a divisibility test for any desired positive integer.
My TI-30XIIS gives thenine (9) digit answer without breaking a sweat, so your comment about tall tales is bullshit! In fact, it is able to display number of ten (10) digits. So, suck it Math Wrath guy!
Why do you say “casted“ instead of “cast“? The past tense of “cast is cast, just as the past tenses of “put” and “hit” are (surprise!) “put”and “hit.” Will your next video say that you “putted” down the answer and it “hitted” the mark accurately?
Other than a curiosity and a great way for mathematicians to waste their time on trivial crap, which seems to be common thing, who really gives a fuck about division by thirty-seven (37)?
2:20 Blud, what's your calculator? 2$ off-brand of an off-brand? Mine can easily reach 10^999... And it's only a high-school one! My Phone's can reach 10^100^100^100!! Who has these low-school/middle-school kind-of calculator on them nowadays?
Well, You are good. But you should abandon filming handwriting, as we are in the era of computers. I suggest filming printed pages. Untill thi... I will watch something else. Butmainly, this is popularizing math. I prefer the original. You are good. So much talk and not one mistake.
Casting out nines to confirm an answer is correct? Hmmmm... I'm not buying it! I think you can discover if a sum is incorrect, but not if it's correct.
Finally, a trick for determining divisibility by 37!
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Once to challenge myself I tryed to purely in my head find all the prime numbers going up to 1000... I eventually got there; after cheating to remember where I left off on the list.
My point being is that it can be hard even with tricks to still do these things in your head.
One trick I did find that was somewhat strange was that 21X21 and 12X12 have reflective answers; OK its been years so maybe its not specifically 12 but when going through double digits you will come across some that do work that way.
Thought of as a kid in middle school while bored and having paper to do simple math repeatedly.
No clue if it has a term already or not.
Is the number 37? Then it is divisible by 37, heuristic solved!
🤣🤣
That's what he said 🤣
How to tell if a number is a multiple of (e^iπ)×-1
Step 1:
Done!
@@Unofficial2048tiles i dont get it
@takingitupto12next e^pi(i)x-1=1 and it says step 1
After finishing with the 999's, if you are left with a three-digit number, you can then cast out 111's until you get to a two-digit number. (Or a one-digit number, or a number between 100 and 110, but let's not get picky.) Just subtract one from each digit at a time. 1⁻¹4⁻¹8⁻¹ -> 037. (⁻¹ is not an exponent here.)
Just subtract the highest multiple of 111 that’s less than N, pretty easy to eyeball that. 111, 222, 333,…888, that leaves you with a number less than 111. Any number less than 111 (3*37) is divisible by 37 only if it’s 0, 37, or 74. If you want the remainder, subtract the largest of those from the your result and you get the remainder mod 37.
I think the only reason why I was recommended thiz is because I sometimes watch videos on niche math theorems and happened to be watching Nintendo related content earlier.
How is Nintendo relevant? Half the way through, I realized Pikmin music was playing.
Zelda music was playing earlier on too
piklopedia 🕺🕺
Fun fact: the process of casting out nines, when iterated on a number (as demonstrated in the video), is essentially the same process as finding the digital root. You add up every digit, take the result, then repeat (iterate) if the result has multiple digits, until you end up with a single digit, which is your digital root. The only thing different from casting out nines is that unless you start with 0, a number divisible by 9 will have the digital root of 9 (in casting out nines, the result would be 0).
I actually decided to make this video as an offshoot of working on a video about digital roots. Will come back to the digital root video at some point, but figured casting out 9s deserved its own video!
I was thinking exactly the same!
I believe that by only adding every digit we spare the other operation, like cheking for 9's (which by itself is a complex operation which involves adding + comparison + substracting/casting out). Thus, with only a simple operation (adding) we can get a faster result with less resources (CPU power).
However, I guess this is usefull when trying to optimize computer code but for other purposes, like math studies, going the extra mile might be worting.
So if my math is telling me anything, wouldn't this trick for 37 also work for 27?
*@[**12:50**]:* By the way, another way to detect errors is to use estimates. For example, you can assume 874 + 397 is going to around 1100 or 1200.
I figured out Casting Out 9s in high school. Great trick for the SATa. Works for multiplication too!
21:47 or you could just take 999 from 1002 which is 3, you're casting out a 999
He could, but sometimes it's better to take the problem to its general conclusion as it gives complete picture.
At that point i took the trick of "borrowing" a 750 to add to the 249 to make a 999 with 3 left over. 😊
This is really cool. Apparently you can just mess with numbers like that, and in any order, to determine if it’s a multiple of 37? Feels like magic!
This is why i decided to go into engineering. Math just feels like magic sometimes, and yet time and time again, it proves to be more useful than we even considered.
For example, black holes were originally theorized in 1796 (by Laplace, whoda thought?), were modeled mathematically in 1916 by Schwarzschild, but they weren't widely accepted as real until the 1970s, and now we have pictures of them!
Math is sorcery
Because in the last 1000 years the 37 has risen to become the absolute superstar of all divisions!
Divisible by 10 to result into an integer. Everything is divisible by anything. You just won't always get whole numbers.
That's not an error. That's just indicating a natural log.
Could you make a video proving this? I know it has a name, but I can’t think of what it is called right now. Basically can you make a video proving that n squared is always one greater than (n-1)(n+1)? For example, 2^2 is 1 greater than (2-1)(2+1). 4 is one more than 3.
It’s because (n-1)(n+1)=n^2+n-n-1=n^2-1
my brain does weird things sometimes. finds the remainders of random numbers after dividing by specifically factors of 999, like 37 and 27. quite cool to actually see a video talking about this weird obsession i have
in other words.
1) split the number into groups of 3 digits.
2) sum all the numbers from step 1.
3) cast out nines.
4) remember all numbers less than 999 that can be divided by 37. 😅
unless... you remember that 37*3=111 so we can further reduce the number taking 1 from every position.
for example: 148-111=37
it's still a pita for some numbers but it can help to further reduce how many multiples of 37 we need to remember.
yay 8 mins!!! thats like a composite number!!
How to determine if a number is divisible by 37
1. Convert the number to 37
2. If the last digit is 0 it is divisible by 37
3. profit
Finally, Aryabhatta!
37*27 =999 , therefore 1000 is congruent to 1 modulo 37
19:45 ah yes, the prime factorisations of numbers one less than powers of ten. Classic.
Even numbers are kinda arbitrary. a base 12 system would easily have a third and fourth layer
I've only ever heard of this casting out 9s trick being used to test if the number is divisible by 3 or 9. If it is divisible by 9, casting out 9s gives a zero. If there's anything left over after casting out 9s, it's not divisible by 9 and what is left over is the remainder after dividing by 9. If that remainder is 3 or 6, the number is divisible by 3.
I've never heard of it being used as a "check your answer" trick or a divisibility by 11 or 37 trick. The one trick I have heard of for divisibility by 11 is to take the sum of the digits in the odd places and subtract the sum of the digits in the even places and if that difference is divisible by 11, the original number is too.
Yeah I think most people learn about adding digits for divisibility by 3 and 9, but we can push it a lot further!
So, could this be extended to casting out 9999 to test divisibility by 101? or 99999 for 369?
by "casting out the 9s", did you mean getting the remainder of a number mod 9? Thank you.
I was smelling marker the whole time. What a wild trick!
! like the Hitch Hikes Guide to the Galaxy number of 42. How long would it take to double your money with interest? At 6% its 7 years multiply years by interest and the answer must be 42.
Amazing tricks bro
This is going to save me _hundreds_ of hours every week!
Lovin the longer video
It is literally 12:37, I think I'm losing my mind, mindblowing coincidences
You keep making mistakes in your casting out of nines. I mean, technically they end up working out but it is a poor demonstration because you keep missing other nights you could have cast out.
51 is also divisible by 10. If you didn’t know that, you might want to try something other than math.
2:16 for me i just put the numbers under each other to add
The wrath of math made chill by some David Wise ambience.
2:16 I found the sum mentally, but that addition CAN be done on the calculator. We can see that the solution will be ten digits in length, and the calculator simply truncated the number and cut off the last digit.
We can see that the units digits, when added together, give us a unit digit of 1. So we tack that 1 onto the end of the solution shown in the display.
This is kinda off topic, but is the music in the background of the video an arrangement of Xenoblade Chronicles OST - Valak Mountain (Night). It sounds pretty much the same except for the music in this video has less instruments so its a more gentle arrangement of that song. If I am wrong, does anyone know what the song playing is?
I tried this trick with the number of ppl who have clicked on this video and added those three digit numbers together (00X + XXX) . I got 635.
000 + 635 is 635. I still don't know if clicks on video was divisible by 37.
Then I tried subtracting 100 * 37 from the number and try the trick from there. I got 933. Just as insightful as the last try, wtf!
But after like 10 seconds of thought, I realized that 933 is pretty close to 999, so adding 2 * 37 added to 933 and compare those numbers should give you the mod remainder. So 1007. 8 should be the remainder. But it took me minutes to figure out so I don't think it is a nice trick. You can reverse engineer my calculation more easily to figure out the view count I saw.
I think I’ll just stick to the bus stop method 😭🙏
Suit yourself 😂
This is why 37 is one of my favorite numbers. First one being 23
23 has importance in Islam and I'm Muslim so I like 23 too!
My favorite number is 277777788888899 tho
@justsaadunoyeah1234 bruuhhh, anyways, the reason why 23 is my favorite number is because i like the way it looks, My birthday being December 23 and all about the Birthday Paradox
@ronaldjacob23 oh ye I forgot about the birthday paradox
What about base 37 system? I have one...
I'm a worldbuilder, and people of my world can check divisibility by 37 easer. Because they use base 37 system.
Gronk aproves
i'm trying to understand the joke and wondering if you know Gronk wore 87, not 37, but maybe you mean something else altogether
Casting out the 9s tells us the last digit is correct. So 90% of incorrect answers would be ruled out using this method.
Veritasium would be proud
Every number is divisible because of decimals, fractions, and percentage numbers.
0:38 2.7
7:37 bro sped up sounds like Ben Shapiro 😭
Do 57 next
Whoever writes these stories has a great imagination.
It seems to me that the whole vid is related to digital Encryption ??
Great. Now I have yet another rabbit hole to delve into with Fibonacci.
a very good pun
Of course it had to be 37
Veritasium referenc
37 minutes ago!
past of cast is cast not casted
If you broke the language would it be in a pastercast?
can we always find n for all primes p such that p/(10^n-1)
except 2
i think if you choose n = p-1
and p 2 and 5 then
10^(p-1) is congruent to 1 mod p
so 10^n -1 congruent 1-1 = 0 mod p
(by fermat's little theorem)
Wdym "p/(10^n-1)" what does that equal
@@tonyhaddad1394???? what do u mean ????
So p is some prime number and n is p-1, but I am not sure what you’re trying to “find”. The “n” itself seems to be part of the fraction. What does that fraction equates to?
3 x 37 = 111. 18 x 37 = 666.
Why did you say “casted”? The past tense of “cast” is “cast, just as the past tenses of “put” and “hit” are (surprise!) “put”and “hit.” Will your next video say that you “putted” down the answer and it “hitted” the mark accurately?
i know the past tense of cast is cast, but it doesn't sound like past tense, by saying 'casted' it is clearly past tense, even if not technically correct, so the listener knows i am referring to something we already did, not something we must now do. yes my next video will say that
@ Thank you. On your then, shouldn’t you also be saying “putted” and “hitted” and “cutted”?
@@KateGladstoneI thoughted that was wrong.
5:00 Whoa!
2:26 It's not tall tales, my calculator is 12 digits.
don't believe it, i've never seen a TI-108 that does that
@@WrathofMath But have you seen one running Doom?
@@christianloder8127 I don't use doom, as you can tell by my username, I'm Indian, so I use Indian calculators.
@WrathofMath As you can tell by my username, I'm Indian, so I use Indian calculators.
Ah I see 1000A + B == 1000A + B + 999B == 1000A + 1000B == 1000(A + B) (mod 37)
Alternatively, 1000A + B = 999A + A + B = 37*(27A) + (A+B) == A+B mod 37
These are good and valuable tricks, and well presented. But at about the 2:20 mark, the lecturer dismisses as “a tall tale“ the existence of calculators that can handle more than eight digits, and that’s ridiculous! That little T.I. calculator he’s using was left in the dust long ago. My iPhone is an SE model quite a few years old, and its scientific calculator can handle numbers of up to 16 digits.
Divisibility tests for several different numbers are mentioned and explained in this talk, which is all well and good. But it should be noted that these numbers are in no way unique for having divisibility tests; in fact, it is not difficult to construct a divisibility test for any desired positive integer.
It was a joke.
no there are no calculators that can calculate past 8 digits. duh
14:24 oh no
I’m in the thick of it 0:00
💻 💍 🖊️ 🤴 👑 💎 😈 📞
37? Why choose 37 exactly? idk, to me seems like a random (😏) number
hi viewer! try to find the reference in the comment above! :)
Veriditium ain't it?
Veritasium reference, nice 😏
37? that's pretty random.
Is the number a multiple of 37? If yes, the number is divisible by 37. You’re welcome!
My TI-30XIIS gives thenine (9) digit answer without breaking a sweat, so your comment about tall tales is bullshit! In fact, it is able to display number of ten (10) digits. So, suck it Math Wrath guy!
1/137
1000/37
Why do you say “casted“ instead of “cast“? The past tense of “cast is cast, just as the past tenses of “put” and “hit” are (surprise!) “put”and “hit.” Will your next video say that you “putted” down the answer and it “hitted” the mark accurately?
37!!!
Other than a curiosity and a great way for mathematicians to waste their time on trivial crap, which seems to be common thing, who really gives a fuck about division by thirty-seven (37)?
Surprised you wasted time looking at this!
2:20 Blud, what's your calculator? 2$ off-brand of an off-brand?
Mine can easily reach 10^999... And it's only a high-school one!
My Phone's can reach 10^100^100^100!!
Who has these low-school/middle-school kind-of calculator on them nowadays?
off-brand? no, it's the only calculator there is, the TI-108. I have over 30 of them
@@WrathofMath I was a bit sarcastic. I know it's an official one.
I have a Numwork, for the high-school one.
Sorry if I was mean btw
A 1000? Roblox Doors Reference
Six minutes lets gooo
Swag route less goooueuu
2:27 my calculator app can do way more than that!
No way!
How much sharpie have you smelled in your life?
i've never smelled a sharpie!
Well, You are good.
But you should abandon filming handwriting, as we are in the era of computers.
I suggest filming printed pages.
Untill thi... I will watch something else. Butmainly, this is popularizing math. I prefer the original.
You are good. So much talk and not one mistake.
He casted it well.
¿ casted? Americans need to learn English 😂
Casting out nines to confirm an answer is correct? Hmmmm... I'm not buying it! I think you can discover if a sum is incorrect, but not if it's correct.
Yes, he says this at 11:30
222/37
6