is 101 a prime number
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all right in this particular video clip I want to show you how we can confirm whether 101 is a prime number or not because it it looks kind of difficult to me thats a pretty big number so lets go ahead and start get started with this okay and we start with 101 and we say 1/3 and 101 is to a factor of 101 no because you know 101 divided by 2 is 15 with a remainder of 1 then we try 101 divided by 3 we already know it is not divisible by 3 because when you add up the digits 1 plus 0 plus 1 it is 2 and 2 is not divisible by 3 but you know well go ahead and you
know do it anyway this is 33 with a remainder of 2 should we try 4 no we dont need to try four because once you know that – is not a prime factor of a number 4 which is a multiple of 2 can that possibly be a be a factor of 101 so well skip all the composite numbers well skip to 5 101 divided by 5 is 20 with a remainder of 1 so that means 5 is not a factor of 101 the next prime number is its not 6 6 is a composite number it is 7 thats right Wonder and 101 divided by 7 is mmm what do you think its 1 4 so its 14 with a remainder of 3
well that means 7 is not a prime factor of 101 the next one up is definitely not 8 because 8 is a multiple of 2 how about 9 now 9 is not a prime number either because 9 is 3 times 3 10 is not a prime number it is 2 times 5 so the next one up is actually 11 101 divided by 11 is what M it is 9 with a remainder of 2 and you know what I can stop right now and I can say 101 is prime now how do I know so quickly that 101 is prime how about the other prime numbers what about 13 what about 17 what about 23 how come I dont even need to try
those things well as it turns out you know what we need to do is to try out prime numbers until the number that we tried or the square of the number that we try is greater than the number itself greater than 101 so in this case we can say that since 11 times 11 is 121 and 121 is greater than 101 we know that 101 is prime now this is a nifty trick because this means that we only have to try out prime numbers to approximately the square root of a number to confirm that a number is prime okay and in the next video clip we can you know use another example to illustrate you know how powerful this little technique is
prime number, math
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