Hey Vsauce, Michael here. You probably think that Iraqi government is stable and legitimate, well think again, there are multiple claims and today we are going to ignite them and see how many new countries will pop up on the map.
How to get your maths answer: 1. Ask any asian friend (preferably Chinese or Indian) 2. If that doesn't work ask your teacher... 3. You're in a test? Try and remember this video you watched 9 months ago 4. Wait... nvm I can just Google it...
No, it’s just that no one had come up with one back then. And honestly, the trick that Michael shows in this video isn’t a quick rule at all. Very time consuming. At that point it is faster to just divide the number by 7.
@@davidcole2913 I have a book from 1960 that shows a divisibility by 7 rule, though it's sort of complex. You have to match up six digits in the number to the series 132 645, working from the rightmost digit first. If your number is larger than six digits you start the 132 645 series again. Each digit in the series is multiplied by the corresponding number in the answer. For 362,880, working from the right, you'd get (1x0) + (3x8) + (2x8) + (6x2) + (4x6) + (5x3) = 91. Then you divide THAT by 7 and get a zero remainder. I think it's easier to just divide the number by 7 straight through, especially if you are doing the problem mentally.
@@jeffw1267 @jeffw1267 Double the last digit and subtract it from the remaining digits. Ex. 434 => 43 - 2(4) = 35, which is 7x5, so 434 is divisible by 7. Using Michael's method, 1/10(abc - c) - 2c 0.1abc - 0.1c - 2c 0.1abc - 2.1c 10(0.1abc - 2.1c) = abc - 21c 21c is just 7(3c), so it checks out.
Divisibility by each number: 2: Number is even i.e. last digit is 2,4,6,8,0 3: Sum of digits is a multiple of 3 4: Last 2 digits divisible by 4 5: Last digit is a 5 or a 0 6: Number is even and Sum of digits is a multiple of 3 7: Take 5× last digit and add to remaining digits OR take 2× last digit and subtract from remaining digits. Final total divisible by 7 8: Last 3 digits are divisible by 8 9: Sum of digits is a multiple of 9 10: Last digit is a 0 11: Alternate between Adding/Subtracting digits from left to right starting with Subtracting. Final value is 0 or divisible by 11 12: Last 2 digits divisible by 4 AND Sum of digits is a multiple of 3
@@natant927 It's because 6 has a factor of 2 ie. 6 = 2 * 3. This means that if a number is divisible by 6 then it must be even so it doesn't make sense to repeat the divisibility by 2 rule
@@aryyancarman705 it did kinda called dong something you can Do Online Now Guys Before it was reffering to uhhh the thing and its called ding now. I think anyways lol
There's a trick for 7 that's even easier: Separate the ones digit from the rest, double the ones digit, then subtract the 2 numbers. Here are some examples 903 separates into 90 and 3, double 3 to get 6, 90 - 6 = 84 which is divisible by 7. (903 = 7 x 129) 3171 separates into 317 and 1, double 1 to get 2, 317 - 2 = 315, which splits into 31 and 5, double 5 for 10, 31-10=21 which is divisible by 7. (3171 = 7 x 453) Note: If this process gives you 0, the original number is also divisible by 7
Oohhh, this is interesting. I suppose this is because adding -2 is the same as adding 5 modulo 7. As far as 7 is concerned, this is essentially the same as adding 5 times the last digit. Brilliant!
eventhorizon51 The reasoning is very similar. I am going to use three digits for the sake of simplicity for this proof, but it trivially generalizes to any number of digits larger than 2 via induction. Any 3-digit number is given by x = 100d(2) + 10d(1) + d(0), where d(i) is between 0 and 9 inclusive, except for d(2) excluding 0. The proposed method is 10d(2) + d(1) - 2d(0), but it works because 10d(2) + d(1) = (100d(2) + 10d(1))/10 = (100d(2) + 10d(1) + d(0) - d(0))/10 = (x - d(0))/10, and (x - d(0))/10 - 2d(0) = x/10 - 2.1d(0) = (x - 21d(0))/10, and 21 is divisible by 7.
This is also a much more useful shortcut if for some reason you don't have a calculator on hand. The one shown in the video is cool and all, but it's not very user friendly for larger numbers, not to mention having a bit of a complex process to it. This is a lot simpler and easier to follow.
@@Aw3som3-117 I suppose only having to multiply by two will generate easier computations, so it might be slightly easier and faster than Michael's method.
@@kickowegranie3200 That is true, because 8 and 9 are not primes, and can thus be written has factors of the previous numbers, thus 7! is divisible by those as well.
We can create multiple methods to solve the 7 one. Like multiplying unit digit by 1.5 and adding it to the rest should also work bcoz 1.5 - 0.1 is 1.4 But using whole numbers like 2 or 5 makes more sense I agree
You can also, for example if the number is abcdefgh, look at h+3*g+2*f-e-3*d-2*c+b+3*a. Basically, going from the least significant to most significant digit you just repeat 1, 3, 2, -1, -3, -2. Much easier to do than the method shown in the video. As a bonus, all the other divisibility rules also preserve the remainder when divided by that number(for example, the sum of digits of 582 is 15 so it has a remainder of 6 when divided by 9). The rule for 7 shown in the video doesn't preserve the remainder, but this one does(but keep in mind that the remainder of -1 is 6, not 1).
o o o o o o o o o o o o o o o o o o o o o_ o o o o o o o o o o o o o o o o o o o o o_ o o o o o o o Seven rows and seven columns. Count the o's and then you've got 'em.
Not related message from a random Hongkonger for anyone watching: Remember the Virus is creating in China, it is all okay to call it China Virus. Never trust WHO cuz it is controlled by CCP.
Michael thank you for all of your Vsauce, Mindfield and Ding videos! The content is some of the most fascinating stuff I've watched on the whole internet. Your method of presentation and your subtle humor makes for a really enjoyable experience.
Yup, let's study to keep graduation possible (ahem homeschool) - internet available - free will available - no teacher peeking for rule breaking - school rules : no rules, games
@@CRAIGC55 Well, then people must feed animals the right way, make special meal schedules, and redo the FRIKKING BIOLOGI, viruses are here because they are predictors too, imagine life 200 000 years ago but in the kingdom of bacteria, viruses, cells, whatever nothing has changed
@@mrghostlyr1162 Viruses thrive off of bad cells. If you have been eating dirty for years, you will be a breeding ground for illness. If you remove the bad cells, virus has nowhere to live. Minimal place to live at best.
This is the first time even in my life im watching a pure math video not because of school but because I wanted to... WOW, Michael really is powerful lmao
My favorite part of my Number Theory elective in college was proving the divisibility rules for 3 6 and 9. They seem so not math-y when you learn them as a kid, but the proof is very easy to understand
I go back and watch this video over and over again simply because the explanations for how it all works is absolutely beautiful, and of course Michael talking about anything always makes it better too
Ok I'm kinda embarassed to ask this but... so I'm pretty good at english becouse I'm learning it since I was 6 but I still don't understand what "Or do I" meme means
@@antonioocchipinti801 No need to be embarrassed about that! It's something Michael say A LOT in his videos. That's all! 😃 Watch a few more from VSauce and you'll see what we're talking about!
antonio occhipinti the ‘or do i?’ meme uses sarcasm. Sarcasm is a type of humour that becomes funny by doing something unexpected. Like saying (insert random dictator here) did nothing wrong. The joke teller doesn’t think that that person did nothing wrong, but its so unexpected and rude that it becomes funny.
I remember watching this when it came out. I didn't understand it back then but now after some algebra, and now calculus, This actually makes a lot of sense.
At first I thought he was talking about all of us watching this video together. More and more, I am convinced that Michael is talking about the math itself. The math is our new math friends.
Divisibility in base 6: *1* If the number ends in the ones place, then the number is divisible by 1. (same as 1 in base 10) 1:08 *2* If the number ends in 0, 2, or 4, then the number is divisible by 2. (same as 2 in base 10) 1:14 *3* If the number ends in 0 or 3, then the number is divisible by 3. (same as 5 in base 10, but replaced by 3) 1:17 *4* If the sum of the ones place digit and the double of the tens place digit is divisible by 4, then the number is divisible by 4. (same as 4 in base 10) 3:17 *5* If the sum of the digits is divisible by 5, then the number is divisible by 5. (same as 9 in base 10, but replaced by 5) 2:29
Actually, there are divisibility tests for 7 that are simpler provided you have a fixed number of digits to work with. For example, if I want to work with 3 digits, then any number will expressible as 100a + 10b + c. 98a + 7b will always be divisible by 7, because 98 is divisible by 7, since 98 = 70 + 28, and 28 is divisible by 7. Therefore, one only need check if 2a + 3b + c is divisible by 7 to check if your 3-digit number is divisible by 7. The problem is that this does not generalize as easily to any other number of digits. For example, if you want to check for 4 digits, as in 1000a + 100b + 10c + d, you instead have to check if 6a + 2b + 3c + d is divisible by 7. In other words, the quantity you have to check depends on the number of digits. This does not require recursion, but it trades for having infinitely many rules, one for each number of digits.
@@angelmendez-rivera351 i was gonna say calm down its just a joke but that's actually a really cool point. It's not immediately obvious why 7 causes so many issues
@@melovepeas The reason is that 7 is prime, and thus coprime with 10 (it shares no common factors with 10 other than 1). But, you say, it works with multiples of 3 ! And that's because 10 is 1 away from a multiple of three, which is actually a very special thing. Basically, there's no general rule... unless there is one. That is, it only works in special cases and in general you just have to go the recursive route. It's amazing how many things we take for granted about numbers when a lot of properties we think as intrinsic to the numbers themselves are actually dependent on the base being used.
The way I was always taught to find a multiple of 7 is to double the last digit and subtract it from the rest of the number. 14 = 8 - 1 = 7 49 = 18 - 4 = 14 = 7 798 = 79 - 16 = 63 = 7
don't abuse the equal sign like that You can do this 7 | 63 "7 divides 63" or for the other way around, "63 dibisible by 7" i remember using in school three vertical dots like 63 :7 but with this unicode character VERTICAL ELLIPSIS (U+22EE) lookup the code. or like this 63 % 7 = 0 (modulo operation result )
@@Dm3qXY - It would have been far too long to type what I wanted to say, and I'm just here for fun... I think it makes enough sense once the numbers get smaller.
This is exactly what I needed. The finals from last semester were delayed and they'll be soon, and this is a perfect way to remind myself about divisibility rules.
Relevant trivia: The number 2520 is the smallest number that's divisible by 1-10. Edit: It also has many other interesting properties such as being: - half of 7! (7 factorial) - a highly composite number (if you don't know what that is you may want to watch this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2JM2oImb9Qg.html) - a colossally abundant number (I've tried to find and video or website that explains it in an understandable way but I can't find one) - a Harshad number (a number that is divisible by the sum of its digits. Ex. 24: 2+4=6, and 24 is divisible by 6) - the aliquot sum of 1080 (a rare relationship between two numbers where the sum of one of their factors is equal to the second number and the sum of the factors of the second number is equal to the first number. If I didn't explain it well I recommend watching until 1:30 of this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-WtbkBl7ct4I.html)
@Wouter vanR I prefer Tau over Pi but I kind of feel bad for Pi this year; nearly everyone forgot about Pi day because of the coronavirus Edit: grammar
I got halfway through the video and Michael is showing us why these tricks work , I began to realize that this is how I do work in my head instead of writing it all down. this is the way I simplify the work so that I can do it in my head instead of having to work it all out on paper
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Not exactly a divisibility rule, but: To check if a number is prime, you only have to check all primes up to its square root. For example: is 103 prime? It’s square root is between 10 and 11, so check 2, 3, 5, and 7. We know it’s odd and doesn’t end in 5 or 0, and that 1+0+3 =4. The only one left is 7, which we test with the trick in the video: 10 + 5(3) = 25, so 103 is not divisible by 7 and is therefore prime.
@@akkok5059 First why do we only check divisibility with prime numbers? Because non prime numbers can be written as the product of prime numbers. Why is that? Because if your number is divisible by a non prime number, you can divide the factor once more until only prime numbers remain. For example, let's take 20. 20=2×10. But 10 is non prime which means you can divide it. 10=2×5. In the end, 20=2×2×5. You only need to check prime numbers to know if your number is prime. The only prime numbers below 10 are 2, 3, 5 and 7.
@@akkok5059 Because the rest of numbers between 1 and 10 are product of primes. Take the number 103 and check divisibility by 2, then 3. Now we have 4, but if the number is divisible by 4 then it's also divisible by 2 and we checked that already. Next comes 5, then 6 but if the number is divisible by 6 then it's also divisible by 2 and 3 - we checked that already.
Michael! I though of a way faster method to check divisibility by 7: 1. Take the leading two digits of the number. 2. Divide by 7 and find the remainder. 3. The remainder becomes the new leading term 4. Repeat until you recognize the number as divisible by 7 or not. E.g. 362,880: Not sure if divisible by 7 36->1 12,880: Not sure 12->5 5,880: Not sure 58->2 280: Pretty sure 28->0 0: Divisible by 7
Michael: now let’s see if it’s divisible by four. My brain: oh yes, we can half it twice. Michael: take the first number in the two digit number and double then add it to the second digit. Me:...
For those of you who forgot the rules as soon as you stopped watching: 2: If the number is even, it can be divided by 2 3:Take all the digits in a given number and sum them up. If the resulting number is divisible by 3, the original number is divisible by 3 4: If the last 2 digits of the number form a number that is divisible by 4, the whole number is. OR. Take the 10s digit and double it, and then add to that the ones digit. If that number is divisible by 4, the original number is as well. 5: If the number ends in 0 or 5, it's divisible by 5 6: If the number is divisible by 3 and is even, it is divisible by 6 7: Take the 1s digit, and multiply it by 5. Then, add to it the remaining numbers as if it were its own number (the whole thing, not each individual digit). If the resulting number is divisible by 7, the original number is as well. 8: Take the hundreds digit, and multiply it by 4. To that, add the tens digit times 2. To that, add the ones digit. If the resulting number is divisible by 8, the original number is divisible by 8. 9: If the sum of all of the digits in a number is divisible by 9, the original number is divisible by 9 REMEMBER: All of these processes can be done multiple times if you are unsure if the resulting number is divisible by the number (1, 2, 3... ,9)
Also, popcorn with a capital "P", which implies it's either someone's name, or a place's name. You can't carry a place around -or can you?- , so I guess they watched with a friend?
i learned a lot of these as a kid and one favorite pastime of mine is to mentally add the digits on license plate numbers to determine whether or not they're divisible by 9 (license plates in my country always have a 4 digit number in them)
@@rjkzk If "That Guy" can help me out please, I'm trying to learn more about the english language. Technically that's not more than one second, so should it be "0.1354 second"?
Michael: "...But how do these tricks work?" Music: "..." Me: "...Wait, what- nothing??? Wow, I have never felt the absence of the Vsauce music so keenly..."
Legit did the same thing. I routinely eat snacks or meals while I watch videos, but opted out of doing that with this one so I could pay attention to it.
As someone with dyscalculia, this is INCREDIBLY helpful. I wish Micheal had been my math teacher! I need to understand HOW math works, otherwise it's too abstract for me. When I was a kid we were expected to just memorize everything by rote with zero explanation, so even as an adult I still struggle with basic multiplication and division. Logic and algebra make more sense to me, so this video is a life saver!
Math should _only_ be about understanding how things work. There should be hardly any memorization at all. It sounds like your difficulty with math had more to do with poor teaching methods.
I feel like my foundation for maths were scrambled by just that. We were always taught to memorize recipes rather than understand how they actually work. I wish I hadn't been taught this way.
What if I told you this video *severely* overcomplicates things? I suggest reading about the cyclic groups and modular arithmetic. Makes all these results much more basic and really easy to extend to other numbers.