Algebra

Prime numbers | Factors and multiples | Pre-Algebra | Khan Academy

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In this video I will talk a little more about what It means the prime number And what I hope you will understand in this video It is a simple concept But as you progress in your sporting career You will see that there are somewhat complicated concepts That can be built on the concept of prime number Which includes the idea of \u200b\u200bcoding And it is possible that some encryption that Your computer is using it at the moment, it depends on prime numbers If you don’t know what encryption means You don’t need to worry now Just what you need is to know that prime numbers Somewhat important. So I’ll teach you the prime numbers The concept can be a little confusing But when you learn it with examples, you will see it a little simple The number is prime if it is a natural number For example: 1, 2 or 3 (counting numbers starting with 1) Or you could say “positive integers” It is a natural number that accepts (exactly) the division by two natural numbers: the same number and the number 1 Only these two numbers are divisible If you don’t see this logically, let’s solve some examples Let’s examine some numbers to see if they are prime or not Let’s start with the smallest natural numbers Figure 1. You can say that “number 1 is divisible by 1” And “accepts division by itself”, so number 1 is prime number! But remember, by definition, you should accept (exactly) divide by Two natural numbers. 1 is only accepted for one natural number which is 1 So 1 is not a prime number Let’s go to number 2 The number 2 is divisible by 1 and 2 only So it seems that it meets the requirements for identification He accepts the division (exactly) of two natural numbers On itself and the number 1. So 2 is a prime number I will go over the prime numbers The number 2 is interesting because The only initial even number If you think about it, then any other even number It will accept division by 2, so it will not be a prime number We will think more about this in future videos Let’s check number 3. Number 3 is divisible by 1 and 3 It is not acceptable to divide by any other number It does not accept 2. So 3 is a prime number as well Let’s try number 4 Undoubtedly, the number 4 is divisible by 1 and 4, but it is He also accepts division by the number 2. So he accepts division It has 3 natural numbers: 1, 2, and 4 So it does not meet the definition requirements Let’s try number 5 There is no doubt that the number 5 is divisible by 1 It is not divisible by the numbers 2, 3 and 4 (You can divide 5 by 4, but there will be a remainder) It is also clear that he accepts division by himself So again, 5 accepts the division (exactly) by two natural numbers: 1 and 5 So again, the number 5 is a prime number. Let’s continue So we see if there is some kind of stereotype here And maybe then I will try a difficult number That people stumble upon. So let’s try the number 6 He accepts the division by the numbers 1, 2, 3, and 6 So it has 4 natural number factors I think you can say it that way So it does not divide (exactly) by two It has 4, so it is not a prime number Let’s go to number 7 Number 7 accepts division by 1, and division by numbers 2, 3, 4, 5, and 6 not acceptable But it also accepts division by 7 So the number 7 is a prime number. I think you understood the general idea here How many natural numbers are numbers like 1, 2, 3, 4, or 5 The numbers you learned when you were two years old Which does not include zero, and does not include negative numbers It does not include fractions and does not include deaf numbers And decimal numbers and the rest of the numbers Only familiar positive numbers If you only have two numbers of them If you accept division by yourself and the number 1 You are a prime number And the way I think If we do not think about the special case related to the number 1 The prime numbers are the building blocks of numbers You can’t break it down any more They look like atoms If you think about what are the atoms Or what people thought about the atoms the first time They think they are those things That cannot be further fragmented We now know that we can actually split atoms If you do, you can make an atomic explosion But it’s the same idea about prime numbers You cannot split it To the product of multiplying smaller natural numbers You can say numbers like 6 are 2 times 3 You can split it, and note, you can split it To the product of prime numbers We sort of split it into its parts You cannot split 7 more All you can say is that 7 equals 1 times 7 In this case, you did not split it further You only have 7 there again You can actually divide the number 6 You can actually divide the number 4 by 2 times 2 Now, based on this method, let’s consider Some larger numbers, and we think Whether these large numbers are prime numbers So let’s try the number 16 So clearly, any natural number is divisible by 1 and by itself So 16 is divisible by 1 and 16 So you will start with the number 2 So that if you can find any other number Then you will realize that you are not a prime number For 16, you can get it by multiplying 2 by 8 Or you get it by multiplying 4 by 4 So it has a lot of factors here The numbers exceed 1 and 16 So 16 is not preliminary. What about number 17? Undoubtedly, 17 accepts division by 17 and 1 It is not acceptable to divide by 2, 3, 4, 5, 6, 7, 8 … etc. None of these numbers or any number between 1 and 17 Leads you to the number 17, so 17 is a prime number And now I will give you a difficult number This number can deceive many people What do you think about number 51? Is 51 prime numbers? If you are interested, you can pause the video here a little And try to find out by yourself If 51 is a prime number If you can find any prime number except 1 or 51 And who accepts 51 divided by it. It seems A rather strange number You might think it is a prime number But now I will give you the answer It is not preliminary, because it also accepts division by 3 and 17 Three times seventeen equals 51 So I hope you now have a good one About prime numbers And I hope we can give you some training on this In future videos or in some exercises

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