So let's talk about one of the key classifications of numbers. And in general, we classify numbers into prime and composite. And so we're going to make the definition. First off, we're going to define the factors of a number. Suppose I have a whole number n that can be expressed as the product of two other whole numbers, p and q. Then I say p and q are called factors of n. And importantly, if p and q are less than n, then they are what we would call the proper factors of n. And this is a very useful definition to keep in mind. Now I'm going to ask a question. We don't actually have to prove the following, but it helps if we think about problems like this one. So here's a number n, and I'm going to write it 33,491 times this other number, 19,871,543. And I want to find two proper factors of n. So let's try to do this as inefficiently as possible. So let's see. Well, I might figure out what this is. And so I'll get out some paper and pencil and do the computation. Actually, I'll go to my favorite search engine here. And so I'll go ahead and multiply 33491 times 1871543. And if I press that, it'll tell me, oh, OK. So here's my product of those two numbers. And so now I want to sit here and stare at this number for a couple of minutes. And try and figure out what can I multiply to get this number? Well, that's a horribly inefficient way of doing this. So maybe we'll be able to do something a little bit better. So let's think about it. Oh, wait a minute. I've already written n as a product of two numbers. You're actually given n as a product of two numbers. And so if you go back to the definition, if I can write n as a product of two numbers, then each of the two numbers are factors. So n is a product of two numbers. So each of these numbers is a factor. And you might make a little bit more thought here. If, by my definition of multiplication, this is this many of these things, then certainly this is smaller than this many of those things. So this number here, 19,871,543, is definitely a proper factor of n. And commutativity allows you to make the same argument. This, 33,491, is also smaller than n. So both of these are, in fact, proper factors. Well, that was an easy warm-up question. So let's take a somewhat more difficult question. So let n be 530 times 36. And I'll find six proper factors of n. Well, here's 2,530, and 36. And again, I can do this using the horribly efficient method. So I'll go ahead and figure out what 530 times 36 is. I get 19,080. And then I sit here and stare for a while at this number and try to figure out what multiplies to that figure. Well, again, somewhat more efficiently. All I really need to do is find two numbers that multiply to n. So if I break these numbers apart, then I can rewrite n as a product of numbers. So for example, 530 times 36. Well, I can keep the 530 and split the 36 into 9 times 4. And so once again, I have n as a product of some things, of 9 and 4 and some other stuff. Or maybe I can try to break the 530 apart into 53 times 10. And so this gives me two more factors, 53 and 10. So now I have my 1, 2, 3, 4, 5, 6 proper factors of my number n. Now this idea of breaking numbers apart by factoring leads to the following important definition, which is of prime and composite numbers. So one important thing, we're going to take whole numbers that are greater than 1. And we're going to call them composite if we can find proper factors other than 1. If we can't find proper factors, then we're going to say that the number is prime. Importantly, we are not defining one to be either prime or composite. And the reason for that we'll see in a moment. So let's consider the problem. We want to prove or disprove that 9 is a prime number. So we either want to show that 9 does have proper factors besides 1 or that no such proper factors exist. And worth noting, we don't know whether 9 is prime or not. We're given a number, and we have to classify it whether it's composite or prime. So we might try to find proper factors, in which case we will not have a prime number. And in this case, 9 is pretty easy to work with. 9 is 3 times 3. And these are proper factors. They're both less than the number. So I have proper factors of 9. And that tells me 9 is not actually a prime number. Now, again, because this is a proved statement, our solution to the problem has to in some way go back to what the definition is. So it might look something like this. Since 9 is 3 times 3, then I have a proper factor. And so 9 is not prime. Actually, it's pretty easy to show that a number is composite. Because all I have to do is to show that I can write it as a product. Primes are more difficult. So here, we're going to prove that 5 is actually a prime number. And so here, we're beginning with the claim that 5 is prime. So let's see if we can prove it. And because it's prime, what I want to do is I want to show that 5 does not have any proper factors other than 1. So let's see. Well, that means that I have to consider every number less than 5 and show that those numbers are not proper factors. So in particular, I have to show that 2, 3, and 4 are not proper factors. Now, again, because the notion of proper factors is part of the definition, I can just make a claim like 2 is not a factor of 5. Hopefully, I'm actually making a true statement here. If this were not true, then my conclusion would be invalid. But if I just want to say 2 is not a factor of 5, as long as I have reason to believe that that statement is true, I don't really have to go into much more detail than this. Again, this is because the concept of factor is part of our definition of the concept of prime. So I can say 2 is not a factor, 3 is not a factor, 4 is not a factor. And so none of the numbers less than 5, with the exception of 1, is a factor of 5. So 5 has no proper factors. And so 5 is a prime number. And again, the important part of the proof that I want to give is the portion that's in green. Now, the proof is actually just a section in green. These are supporting statements. We don't really have to include these as part of the proof. But it's important that they actually be true. So what happens if I consider a number like 127? And if I want to prove that this number is prime? So how would you do that? Well, would you have to do the same thing we did before and verify that no number less than 127 is a proper factor? Well, actually, yes, you have to do this. However, it's possible we might be able to skip some of the lesser numbers. And this leads to a very useful theorem about prime numbers. Any composite number n has a prime factor. So if we want to determine whether a number is composite, we can check to see whether it has prime factors. And the proof of this is actually pretty neat. So we'll go ahead and give a sketch of it. So if n's a composite number, then by definition, I could write n as a product of two numbers, both of which are less than n. And if either of these numbers is prime, we're done. And every now and then, the universe actually gives us an easy problem. And so maybe we do find that one of those numbers is prime and we don't have to go further. But this is often the case. The universe rarely gives us easy problems. So maybe both numbers are composite. Well, what does that mean? Well, if they're composite, that means that I could write both a and b as a product of proper factors. So I could write a, for example, as mn. And because they're proper factors, both of these have to be less than a. And again, we're in a situation, m and n. Well, if either of m or n is prime, we're done. Because then that will be a prime factor of a, which will in turn be a prime factor of n. So if I get two prime numbers or one prime number here, then I'm done with the problem. And again, every now and then, the universe gives us an easy problem. On the other hand, if they're both composite, I can repeat the procedure. And so these are composite numbers, so I can express each of them as a product of two other numbers, both of which are less than m. And so again, if one of these numbers is prime, we're done. If they're both composite, then what I can do is I can continue the problem. And what I end up with is a descending sequence of numbers. I have my initial number n. a is a proper factor, so a is smaller. If a is composite, there's a proper factor m, which has to be smaller than a. If m is composite, there's a proper factor u, which is smaller than m. If u is composite, there's a smaller factor, which is a factor of u. And so on. But because I have a sequence of whole numbers, each of which is smaller than the preceding one, this sequence of whole numbers has to have a last term. Well, the only thing that's going to stop me from finding smaller and smaller numbers is getting one of these numbers eventually to be a prime number. And that's going to be the completion of the fruit. Because sooner or later, I cannot avoid running into a prime number. And once I find that prime number, that's going to be my factor of n. Now, the reason that looking at this proof is useful is that it gives us a somewhat more efficient way of doing a prime factorization. So let's consider the following problem. Find a prime factor of 360. So one thing we might do is we might go through and try and see does two divide, does three divide, and so on. And in some cases, that'll be easy. In other cases, it'll be very tedious and painful. So instead, we can go back to how we did the proof and the proof was find any product of numbers that multiplies to 360. So for example, I might consider 360, 36 times 10. And I check, is this prime, is this prime, or more effectively, can I factor these numbers? And so I might look at 10, for example, and ask myself, well, can I factor 10 or 36? 10's a little easier to factor. So let's go ahead and factor 10. It's 2 times 5. And now I check my numbers. Is 2 prime? And it turns out that 2 is actually a prime number. Likewise, so is 5. And so if I wanted to find a prime factor of 360, I can start with an easy factorization and then continue with the easy factorizations.


Mr. Yim, same question. Are you diverging, are you starting to diverge with your interest with the United States and generally what's your view of the situation? Well thank you Mr. Chair. I mean for the floor. Well it's always a great pleasure for me to be at WPC and you know sitting in the prominent panel like this. Well it's very embarrassing that I was preempted by my old friend I mean you know for the presentation I hope I'm going to make in this panel. Well we worked together a long time ago when we had the first I mean North Korean nuclear crisis. Well Doug was a White House official and I was assigned in Washington working at the Embassy so we had to face I mean the first North Korean crisis but the good thing is that we always you know were on the same page so it was extremely easy to work with Doug which means good you know cooperation between my government and the US administration. Well I think he you know well aptly presented I mean the overview of what's happening you know this year and what happened last year. So last year I was sitting in the same panel saying that South Korea faced the most dangerous national security crisis since the Korean War. Well North Korea continued a provocation by making nuclear bombs and launching long-range missiles. Well there was a dramatic turnaround I mean coming into the beginning of this year. Well as Dr. Pal said I mean President Moon utilized the momentum of the Winter Olympics at Pyongchang in Korea and he induced North Korea to come to the peace process on the Korean Peninsula and invited North Korean leader Kim Jong-un to the summit table. So he succeeded in inducing Kim Jong-un and even succeeded in mediating first ever held summit between the US president and North Korean leader. So everybody was excited I mean to see what would happen when President Trump and Kim Jong-il meet you know in the scheduled the summit. Well we have seen I mean the you know great fanfare and the great I mean you know summit which was held in Singapore and as a North Korean negotiator I had a very high expectations from the result of the summit meeting between President Trump and Kim Jong-un. But I was I mean you know very shocked I mean to see the contents of the Singapore agreement I mean which was printed I mean later. Well I think you know President Trump made the misstep you know in inducing North Korea to the full and complete denuclearization. Well you know if you look at the contents the language I mean they expressed in the statement is the North Korean language not our language. Well South Korea and the United States set the goal I mean for the denuclearization as CVID complete verifiable reversible dismantlement or denuclearization. But what they said is the complete denuclearization of the Korean Peninsula which has been used all the time by North Korea why not North Korea but the whole Korean Peninsula which includes South Korea we don't have nuclear weapons we never developed a nuclear project but the only thing you know we have in South Korea is the US nuclear protection and US nuclear umbrella. So by you know mentioning the complete denuclearization of the Korean Peninsula which means you know well the US should withdraw the nuclear umbrella protection for South Korea and even with the you know North Korean language I mean they agreed well three points number one was to normalize the relations between North Korea and the United States. Number two peace initiative or peace regime to be established on the Korean Peninsula. Number three denuclearization so it gave rise to the sequencing problem North Korea will insist that US must act first I mean to normalize or to have you know well regular relations with North Korea before North Korea moves for denuclearization. So this is the you know problem I mean Mr. Trump I mean well he never understood or I don't know but what happened and well Kim Jong-un was very doing very good job fully assisted by the institutional memory of the North Korean bureaucracy but Mr. Trump I don't know what happened between himself and the very you know capable bureaucrats at the State Department and the DOD so there seems to be some you know gap between the White House and other bureaucratic institutions of the United States. I strongly believe I trust I mean the you know State Department officials and US military and the day I think they will handle I mean this issue well down the road but now Trump I mean Kim Jong-un wants to have second summit with Mr. Trump. Why? Well I think he can play around with Mr. Trump and so he doesn't want to have some working-level negotiations to resolve this issue but he wants to get close to Mr. Trump. I mean you know well Mr. Trump said they are in love and he likes the love letters from Kim Jong-un all the time and keeps the letter in his pocket. Thank you. So well I think still we have impediments obstacles before we realize the full denuclearization of North Korea but we cannot go back to the confrontation you know we saw last year but we have to keep North Korea on the table with our leverage which is international sanctions. We had the two leverages until last year we had the strong military you know combined forces between the United States and South Korea but after the Singapore summit Mr. Trump let it go and the no more combined military exercises between the US forces and South Korean military so we lost one leverage but we still have you know another effective leverage which is international sanctions led by the United States and United Nations so we have to keep going until we see the change of North Korea in a genuine and insincerity. Thank you. Thank you very much.


Soldiers from the 173rd Airborne Brigade Support Battalion were recently invited to speak to a group of enthusiastic students at a school in Circle-Ub-Kirky, Slovenia. They were eager to learn about just America, about how different we are from them. They already know a lot just from the internet and movies and everything like that. If they can see us as normal people, then, you know, I think we have a better future. Charlie Company and the 173rd BSB is currently training with U.S. Air Force and Allied and Partner Nations on field medical care at Circle-Ub-Kirky Air Base as part of Exercise Immediate Response 16. No matter how good of a teacher you are, you can never compare to a native speaker of any language. Really, no YouTube clip or listening activity or reading activity can compare or a movie can compare to real-life experience, so this was really, really good.


It's on Corbett. I'm Rick. What do you do expect after that win congrats India? Jai Hind on beating up on Bangladesh. Now it's on to the semi-finals. Yes So that's very exciting. You're gonna win it all. I know. Yep.   This is called judgmental hi-kai Which sounds like a game doesn't it judgmental hi-kai, but it's too well. It's like highlight But it's a different kind of game and the people that play it would have you pronounce judgmental Because it has two L's. Yeah, I would I would I would pronounce a judge. Why yeah, why is it strange, right? That is that's what I was wondering judgmental hi-kai hi-kia hi-kia. I think it's Kia hi-kia but it has Rush come around. Yes. Yes Newton. Yes the Bose yes, that are alive, right, so he's been in a lot. So this is one of these Yeah, we started to see a bit more of his stuff coming at us So there's a beautiful stupid babies. I do want to watch one of his films. I'm assuming I should watch one before this one Maybe maybe so we'll see yeah, but no idea what this is about. So here and it's coming out next month. We all right Actually this one. It's July. Oh, it is July now Stop see from behind Please This is not normal, people are scared of normal things these days. The way I saw the dali, someone cut the dali. Hey, look at the result of the dali. Keshav is so obsessed. I ate chicken with a stick. So this is why I will give you money for the mutton.   She is crazy. Her mind is on food. Bobby and Yemiga will be taken out of the house in the middle of the night. You can't leave me. You have to do it. I will expose you. Yeah, go. Expose me. I literally thought every single time it was topsy. I did too. That was Hindi. I don't think it was. I don't think it was either. At first it sounded like Hindi, but that's not Hindi. Yeah, I don't think it was. And I don't think it was Tamil. Yeah, I don't think it was either. But I love the character that the girl was putting on. It was very similar to Hindi. Yeah, it was. It might have been a little bit of both. You can tell us, obviously. I mean, I'm hoping our ears have gotten that acclimated to Hindi that we can pick up on the nuances that are that subtle that we realize. Well, one of the big things is that when the poster came up, the whole word judgmental wasn't in English. Right. That is North Indian. Yes. But once again, tell us, please. Who is that actress? Because, one, she looked like topsy. Is it Kanada? And is that how you pronounce that? Kanada? No, that's a country, Rick. That's a language. What? What did it pull up that? Oh, okay. I thought you were talking about the actress. No, no, no. The language.  How? Comedy, drama, mystery. Oh, so I think that the word judgmental is. Yes. People that have mental illness. So it's like a play on it. Yes. She is, oh, okay. Yeah, we've seen her before. She's from Queen. I immediately made me think of Topsy Pinau. Yeah, it did, didn't it? Yeah. That's right. She's the man of Karnika. I was just thinking about that in one of our reactions recently, about how that was one of the first trailers we reacted to. We still haven't seen that movie. Yeah, I know. And we loved it. Yeah, Power Woman. We almost did in theaters and then it left when we were about to see it. That would have been one of the first ones we would have seen. She looks really goodness. The trailer is definitely very weird, but I think that was on purpose. I liked it's weirdness. Yeah, it was definitely very strange. He has this guy, so they say, I need to remember his name. Rajukumar? Rajukumar Rao. Basically everybody says he's one of the best actors out there. I think it's not Rajukumar, but just Rajkumar. Rajkumar? Yeah, Rajkumar Rao, I believe. Three syllables, Rajkumar Rao. And the director is Prakash No. Kovalamudi. Prakash Kovalamudi. I hope that was close. I don't recognize him. Maybe if it's on sometimes like IMDB won't show but maybe Wikipedia will show the breakdown of what the language is. Oh. It reminded me of Bahubali and I'm wondering if, because Bahubali was done in a couple of languages. Let's see here. It says Hindi. That was Hindi? I am so screwed up now. It's a Hindi language black comedy because it sounded like Hindi but in some spots it didn't. I'm freaking out. You agree though, right? Partly sounded Hindi and it was similar but also there were parts in it that made me think it wasn't.  The thing that really threw me was but I knew it was the structure of it with things being forward and after and some of the things it really threw me. I'm so freaked out right now. Well, having those two actors that even though we haven't seen them in, I don't think we've actually watched their work yet except in trailers of course. They're both renowned actors and so I'm hoping and that means this is going to be a really well-acted film. I loved her character in this. I thought it was very corky. Very similar to University that that movie was Zach Galifianakis. It's kind of a funny story. That's what it's called? It's kind of a funny story? I've never heard it. It sounds like Hindi that confused you. They're going to want you to actually talk about the trailer? Oh, this is called The film is called You Just Mess Me Up Anyways, but it's about these people who are still in institution and them dealing with it. It's a dark comedy. Here's what I hope. That's not making light of. No, that one didn't make light. It was very serious. He was a comedian in it and it was about mental illness but still masking everything with humor and all that kind of stuff. But then it also had young people that were dealing with it so I'm wondering if this is going to be very similar in terms of seemingly normal people dealing with mental illness and everybody else dealing with their mental illness and how to treat it. Or how the mental illness is of the normal people. There's a murder in both of it. Yeah, exactly. There's a lot of layers to it. Looks interesting. With the main two actors, even though we haven't seen them I know that they're very respected in the industry. I'm still freaking out over the Hindi thing.


What is good Marvel Squad and welcome back to our channel as you see by the title today? I'm getting crunked and I'm just kidding, but I did already start I got some of my magic drink right in there right now So what's going on today is me and my friend are actually going out to the bar We're not going to like a club, but we're going to like a bar I'm gonna tell Mariah I'm going to a club But I don't see a point of going to a club without your girlfriend because like dude I'm not trying to like get hit on by any girls I'm not trying to do anything that I would regret you already know where I'm getting at with that But my friend is actually about to be here in like in the next five minutes It's still light out, but it's the perfect time to get ready for this prank So what's going on is I'm gonna be going out to the club today club and coming home drunk now Let me just tell you if you've not already guessed yes I'm acting a little bit goofy because I already did start it pregame guys Let me just tell you the drinks at the bars are just so expensive this drink that I'm drinking right now Which by the way do not drink if you're under 21, but the drinks at the bar there's like $15 and I literally made that That's like $3 to make at home. So it just doesn't make sense why I would start at home and then go there And it just be cheaper anyways I'm gonna be coming home Wasted to see how Mariah reacts.  We're watching our show right now I don't want her to get any suspicion. I told her I was taking out the trash And you already know that only takes like two minutes So I hope you guys enjoyed this video make sure to give it a thumbs up for team bill right now And I can't wait to rewatch whatever you're about to see because I'm probably not gonna remember what happened If I am drunk, but we'll just see how it goes. So enjoy the video and I will talk to you guys After I get home from the bar the club. I'm actually gonna leave the camera in the garage So when I come home, I could just pick it right up and go inside or maybe I'll set something up either way I'll figure it out, but enjoy. All right guys. I just got home from the club I was actually at a bar with one of my buddies and it ended up two of his friends ended up showing up So we had a good old night and he didn't pick me up We actually Ubered there and back so don't worry none of us drove but I am home now and it's funny I didn't even remember I had to do this video until I was like halfway home and then I'm like wait I have a camera set up. I have to get into character. Okay, so I'm already super kind of drop like that This is like totally legit, but I'm gonna act double as wasted as I am now to Mariah and Just to see how she reacts. Let's go on at the front door I'm gonna be knocking on the door until she answers and then once I do get inside I'm gonna find a time just to turn on the camera that I have set up because it's not on yet So let's go wish me luck snap at the door already, you know Hey, what up, cutie? What's going on?   Give me a twirl You gonna make me a drink or something? I'm losing my bus. Oh Oh, oh my god, this is so comfy Freakin feeling good. Oh my gosh, come on.   I have a surprise.  I said Look at me with some girl was doing this No Like you just threw the my good shoes. No, don't even try to speak a makeup.  Why are you asking? Oh my god? Okay.   I don't want it. So I was drinking earlier I don't care. I left to go to the club. Are you the one that I'll drink it?  No, you need to get up Do I'm gonna tell you what they did to me?  This is just babe.  Do you guys even care of me when I'm wasted. I'm gonna shrine it to me. Throw me around. Throw me at the couch.  I didn't go to a club. So where'd you go? A bar with Mark and two of his friends Okay, there's many and there were girls Okay with Mark and two of his friends there were guys, there were girls I mean Do you like you did you like your lap dance? No, I didn't Well, you're gonna remember it forever I just turned on the camera Be careful, there's a duck pepper Do you know what my name is pepper you can call me dr. Pepper I just spilled it.  No He just warned me, baby. Give the towels. I have to give the towels. It's gonna stay in our carpet. Why aren't you getting off? This is a cold red This is a cold red. You're this is see this I'm freaking I'm pumped right now. This girl won't even help me clean it up I went I told you I went to a bar. I was just joking about the club It doesn't matter where I went.  Can you baby? This is a crisis.  I do not come home acting like a goof Okay, don't throw me under the bus like that and I never control you.  I wasn't being mean. I'm just very crabby tonight and And I'm not the mood for his BS. I put up trust me. You know what?  I don't know if we even told you guys a story of when he threw up all over himself in the And then he threw up that could be for a story time. That could be for a different story time Yes, so don't think that I don't help him out because I let him just gag on himself. You love me too. Yes Okay, then a little too much pda for the bubble squad and your video bill. All right guys I hope you enjoy this video. Basically what I was filming is just coming home drunk and uh, seeing how you react And I gave you a lap dance too. I gave you a Dr. Pepper. You gave me a lap dance Now it's time for me to go back to bed. How does it feel to get a lap dance from a doctor? Dr. Pepper.  Nasty. You're nasty. Guys, I hope you enjoyed this video. I know this was scrambled But like, you know, what's not to be scrambled when drinks are involved. Once again, thank you so much for watching Make sure to subscribe if you haven't give this video a thumbs up for team bill I have had a great night. How drunk are you? I'm good. I'm like a I'm like a seven and a half out of time It's time to go to bed. No, it's it's still early. It's it's like midnight something like that Yeah, we have a work day tomorrow. So it's time to get back to All right, don't I don't drink a lot like what once a month he'd barely guys he barely drinks He just goes out every once in a while once every other month something like that.  That's it and you're toast You know, I got out that phase out of my life and it makes me you don't have to drink to have fun And I don't drink to have fun.  It's okay. All right. Well, I do it safely. I uber at home. Okay, and I ubered there All right guys, I hope you enjoyed this video once again Hashtag team bill in the comments give it a huge thumbs up for me and mariah and we will see you in the next video But until then Love you guys


Our teams continue to monitor Tropical Storm Nicole. We strategically place crews around the state that are ready to respond. We expect to see rain and high winds over the next day or so. Our teams are ready to respond as quickly and as safely as possible. Please keep you and your family safe.


In one scene, Elvis is shocked to learn of Sharon Tate's murder by members of Charles Manson's cult. Before doing this film, Austin Butler, who portrays Elvis Presley, played Manson family members Charles Tex Watson in Once Upon a Time in Hollywood with Kurt Russell, who not only played the king in Elvis 1979, but also appeared unbilled with Presley in It Happened at the World's Fair 1963. After wrapping up the filming of the movie, Austin Butler was rushed to the hospital where he'd been bedridden due to the virus which simulates appendicitis. Austin Butler and Olivia Dijon's height match almost perfectly with Elvis Presley and Priscilla Presley. Butler is six foot and Dijon is five three. Elvis was five 11 and three quarters and Priscilla was five four. Tom Hanks and Colonel Tom Parker on the other hand have the exact same height at six foot.