Trick 20 - Shortcut for Checking Prime or Composite

hello friends it is rightly said that there are thousands of books written printed and published every year but how many books are read how many books are understood there are so many methods mentioned in our book ancient books in which there were so many calculation shortcuts but we seem to have forgotten most of them today's in pick number 20 I am going to deal with prime numbers which are taught to the students at uni other words and students of higher classes also struggle to spot the prime numbers if they are given a three digit or a four digit number so this concept of finding the prime numbers was say initiated in third century BC and no one of current generation remembers this so I thought I would refresh this method once more and you will realize that it is so easy to spot all the prime numbers from 1 to 100 by utilizing just 15 seconds so here I go what I have done is I have written all numbers from 1 to 100 in rows of 6 so 1 2 fixed 7 to 12 13 to 18 and so on until I complete 100 now when I start spotting the fine numbers the first thing I do is I remember that one is not a prime number it is not a prime number and it is not a composite number as well so we have to forget one now we start from 2 we inserted 2 because 2 is a prime number and we try off all the numbers in this column because all these numbers are even numbers divisible by T similarly for is divisible by 2 so which I lost all numbers which occurred in this column as well similarly 6 is divisible by 2 so all numbers in this column are also cut off so we are left with only 3 columns now so all the prime numbers are going to exist in these three columns only so that solves half of our problems now come to the next number 3 3 is a prime number and another 3 in this column you find all numbers which are multiples of 3 so they cannot be kind they are divisible by P so I write off all numbers in this column as well except 3 of course which is prime now you want to fight for finding numbers divisible by 5 you have to move diagonally just be the table of 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 and 100 so I have struck off all the numbers which were divisible by 5 head so now the last step the move one takes is all ready to talk now 1 2 7 again for finding the multiples of 7 we have to move diagonally 7 14 21 28 35 42 49 56 63 77 784 91 and 98 this is all for this is how we arrived at the numbers all numbers which are encircled all numbers which are remaining these are the 25 prime numbers between 1 and 100 these are the simple and it's so easy to spot the prime numbers one question which arises is why did I stop at 7 and why didn't I miss further see I have taken numbers up to 100 the highest number is 100 and the spoils of 100 is 10 so you just need to consider all prime numbers below 10 that's all so we started from 2 3 5 7 8 & 9 are not prime 10 is not prime so underneath s we have only 4 prime numbers so that's also a subsistence if you have expanded this matrix to 200 then squares of 200 would have been a larger number so you would have considered numbers below that square this number okay let us proceed further now one more problem with which children are facing is while taking LCM suppose they have to make factors of a larger number and they have to identify the factor of a particular number which is quite big so it is a problem for them I take one example and just illustrate suppose we have 277 and we have to check whether 277 is divisible by any number of not now committing factors this is a big problem so I will just tell you one method through which we can tell whether two 77 will be divisible by some number or not now let us see the square is out in 77 of the state is not a perfect square but I will find L numbers whose wire is very near 277 4 in this case we have said 17 well 289 so W is a numbers whose square is very close to that whatever so I will write all time numbers below 17 these are 2 3 5 7 11 13 so only six Pandavas now my task is lesson I have to just check whether some 77 is dividual by these six numbers of not obviously it is not divisible by 2 3 5 7 11 and 13 so 277 is times we don't need to take it by larger numbers say one more example say I have have to check for a ribbon-cutting visited time or not or whether it comes in the table of some smaller numbers I consider under 4 1 3 and I take that 21 square is 440 125 is obviously whole inner digits below this so I have to take a larger number 21 square is 441 so 441 light Rose I suppose one thing now all signed numbers below 29 2 3 5 and 1113 and after 13 we have 17 and 19 as well here's the Camaro 13 so we stopped there 13 here is a number is 21 so we have to prop it nicely now yet formally is not interested not digitally by 2 3 5 but 4 1 3 is divisible by 7 divisible by 7 so if it is tilted by 7 so for one thing is not right so this is a very very useful method when we have to teach children how to spot whether a number is prime or not instead of taking larger numbers of 2 4 1 3 they can spot some unique numbers and check whether this converges visible by these numbers only so a lot of problems will be solved and students will be able to find the LCM of two or more numbers very quickly keep learning keep enjoying share and subscribe the video if you liked it

Channel: Suresh Aggarwal

Views: 495,773

Rating: 4.6599913 out of 5

Keywords: Prime numbers, funny maths, maths shortcuts, increase your calculation speed, tricks in mathematics, speed maths, funny tricks in maths, mathematics fun, shortcuts for competitions

Id: swkC2DSpjAs

Length: 9min 25sec (565 seconds)

Published: Mon May 29 2017