PLAYING WITH NUMBERS | CHAPTER 3|EX 3.6|EASY EXPLANATION|NCERT|INSIGHTFUL MATHS
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00:00hi everyone welcome to insightful maths in today's session we are going to
00:05continue chapter number 3 playing with numbers for grade 6 till now we have
00:10understood the LCM method the prime vectorization and the related terms the
00:15common factors common multiples in this particular exercise we'll be practicing
00:21how to find the highest common factors of the two numbers so let's start the
00:26session before that if you have not liked and subscribed please press the
00:30like button and subscribe to my channel let's start the session okay so question
00:36number one you can see on my screen we have to find the highest common factors
00:40of the given numbers the first numbers the first pair of numbers given is 18
00:45and 48 I'll be using different methods for different questions whichever method
00:51you find easier you may opt for that method okay answer should be correct if
00:56any particular method is mentioned in the examination you have to follow that
01:00method only if nothing is mentioned then it is your comfort level okay so question
01:05number one is we are being given a pair of numbers that is 18 and 48 and we need
01:13to find the highest common factor let us first see the prime factorization
01:18method for finding the highest common factor for that let me just do the prime
01:23factorization of these two numbers one is 18 another one is 48 18 we know that
01:31it's an even number so this is divisible by 2 one more thing I would like to add
01:36prime factorization you have to just pick only the prime numbers to divide
01:42this now this particular number is divisible by 2 and 3 both so it's your
01:48choice if you pick 2 first or 3 first it is not going to change your answer
01:53your answer will still be same so 2 into 9 that's 18 3 into 3 that's 9 again 3
02:03divided by 1 is 3 we are not going to take 1 as it's not a prime number so
02:08what have we got 18 is equal to 2 into 3 into 3 now we are having another number
02:17as 48 48 another it being an even number it is divisible by 2 so 48 divided by 2
02:26it is 2 and 4 24 divided by 2 is 12 12 divided by 2 is 6 and 6 divided by 2 is
02:353 3 divided by 3 is 1 right how many times for 2 we have got 4 times so I can
02:43write 48 as 1 2 3 & 4 along with 1 3 after prime factorization now the most
02:54important step that you have to understand we have to make pair of the
02:59similar factors pairs it should be the number or the factor which is common in
03:04the prime factorization of both now have a look here we are having 2 here and 2
03:11here have we got 1 pair we are having 3 here and 3 here we have got another pair
03:18now I am left with 1 3 here but we do not have any pair for 3 we are having
03:242's here but no 2 at the top so we are having just 2 pairs pair means 2
03:30numbers okay out of each pair take only 1 1 number out
03:361 2 out we have 1 more pair 1 3 out after taking these number out just take the product so 2 multiplied by 3 your answer is 6 that is the highest common factor of 18 and 48 I hope it is understood let us do the b part as well using the same method b part 30 and 42 so what is step
04:06number 1 I am using prime factorization method after that I'll give you one more
04:11easy method that I personally like for even the bigger numbers it is quite
04:15easier now 30 it is divisible by 2 30 divided by 2 is 15 15 is divisible by 3
04:25this is 5 and 5 is divisible by 5 it's 1 now it's a turn for 42 42 being an even
04:34number I can divide this number by 2 so 42 divided by 2 is it 21 21 divided by
04:433 is 7 and 7 divided by 7 is 1 for this once again I request please learn the
04:50tables till at least till 20 for making your calculations faster now 30 can be
04:56written as have a look 2 3 & 5 2 3 & 5 now we have 42 which can be written as
05:062 3 & 7 I hope up till here everyone is aware of what to do after doing prime
05:14factorization let us make the pairs of the common factor we can see here 2 & 2
05:22it's common 3 & 3 is common we do not have any 7 up and 5 down just leave
05:29these numbers out of this pair 1 2 out out of this pair 1 3 out now take the
05:37product 2 multiplied by 3 is 6 and that's your answer easy enough there are
05:43so many parts of this particular question doing each and every part here
05:48is doesn't make any sense because it is basically a practice game right now
05:53let's do one thing I will take this number 18 and 60 will use some other
06:00method for finding the highest common factor now till now I have used prime
06:05factorization now I will be using the division method for the same let's go
06:11ahead now see part is 18 & 60 what I'm going to do bigger number in and smaller
06:19number out 18 out and 60 in 18 now what I'm going to do I have to keep on
06:28dividing it till the time the remainder becomes 0 just observe the steps
06:32carefully and try to do this question yourself you will find it much easier to
06:37find the highest common factor using this method this is 18 now I'm not going
06:43to do it myself I'll show you the calculations if you remember the table
06:47of 18 very well otherwise you need to do the calculations now 18 stable till
06:54which position I have to read to go to 60 18 into 2 is what that is 36 what is
07:0118 into 3 8 into 3 that is 24 2 up 3 into 1 is 3 plus 2 is 5 that is 54 I
07:12cannot go till 14 this 18 into 4 that number will be more than 60 so move
07:19till third position 18 into 3 54 the difference of these two numbers is 6
07:25till here we know now what will happen this remainder will become your new
07:32divisor divisor means the number which divides initially 18 was divisor now 6
07:41is the divisor what will happen new divisor will divide the old divisor that
07:47means 18 now divide 18 by 6 6 into 3 is 18 and we have got the remainder 0 in
07:57the last which number the divisor which gives you the remainder 0 this
08:03particular number is your highest common factor so what is the answer here
08:09highest common factor of 18 and 60 is what this is 6 have a look in just two
08:17simple steps we got our highest common factor let us continue the same method
08:23for D part as well I request stop the video and do it yourself and then check
08:29your answer D part bigger number in smaller number out now let us check what
08:38is 27 into 2 7 into 2 is 40 2 into 2 is 4 plus 1 is 5 we can go till second
08:46position into 2 is 54 quickly get the difference of 63 and 54 it is 9 now what
08:57will happen this is your remainder the remainder becomes new divisor now it
09:03will divide what the previous divisor 27 divide 27 by 9 does it come in the
09:10table of 9 9 into 3 is 27 and the remainder is 0 I told you earlier also
09:17the number which gives me finally the remainder 0 it is your highest common
09:23factor so what is the answer here highest common factor is 9 I'm going to
09:30do one more part for you let me pick the bigger number 34 and 102 will easily
09:37find the highest common factor using the division method once again what we are
09:43going to do bigger number 1 0 in 1 0 2 and 34 out 34 into 3 4 into 3 is 12 3
09:57into 3 is 9 plus 1 is 10 we have got 1 0 2 in one shot only so 34 into 3 is 1 0 2
10:07this number is completely divisible by 34 what does the rule says the number
10:14which gives me the remainder 0 is the highest common factor so what's your
10:18answer here this number 34 is giving me the remainder 0 so your highest common
10:24factor here is 34 good to go all right now let us pick the last part where 3
10:33numbers are being given I suggest where more than 2 numbers are there use prime
10:38factorization method only that is going to help you out prime factorization of
10:4512 45 and 75 after that we will be making pairs of the common factor all
10:52right 12 being an even number 2 into 6 12 2 into 3 6 and 3 into 1 is 3 45 again
11:02it's a multiple of 3 as well as 5 it's your choice if you wish to start with
11:083 or 5 3 into 1 is 3 5 15 3 into 5 is 15 5 into 1 is 5 75 once again it's a
11:21multiple of 3 let's divide this number by 3 first 3 into 2 is 6 3 into 5 15 5
11:31into 5 25 5 into 1 is 5 good to go till here now let us write it in this format
11:3812 is what 2 into 2 into 3 2 into 2 into 3 what is 45 we'll write here that is 3
11:49into 3 into 5 now the last one 75 is 3 into 5 into 5 right prime factorization
11:59is being done and I have written it in this format which factor is formal in
12:04all three let's have a look is too common we don't have to in 45 and 75 it
12:11is not common do we have three formal we have one three here one three here and
12:17one three here so this is one pair out of this pair right the number which is
12:24common in all you just need to take it once out this is one pair I have taken
12:30three out do we have five formal please understand five is common in these two
12:35but we do not have five in twelve we cannot take five whichever factor we are
12:41picking it should be common in all three so what is the highest common factor
12:46here your answer is three I hope it is easy enough let's move to the second
12:52question what is the highest common factor of two consecutive now three
12:58options are given to us in my previous videos also I told you what is the
13:04meaning of consecutive consecutive means one after the other if I talk about a
13:10part consecutive numbers it means one after the other one two three four five
13:17and so on what is the highest common factor of two consecutive numbers let's
13:23take an example two what is the what are the factors of two just one and two what
13:30are the factors of three it is one and three which factor is common in both
13:35only one that's the answer let's check for three and four factors of three one
13:43and three factors of four it is one two and four which factor is common in both
13:50it is again one let us check for another combination let's say four and five
13:56factors of four one two and four five again being a prime number factor is one
14:03and five which is common one once again so what conclusion we can draw out of
14:09this the highest common factor of any two consecutive numbers is always one it
14:17goes true for any pair of numbers provided they are consecutive they're
14:23coming one after the other one more thing you have to keep in mind if there
14:28is nothing common between two numbers one is the highest common factor it
14:33cannot be zero because one is the factor of every number so if nothing is common
14:39at least one is for correct so answer of a part what is the highest common factor
14:45it is one second part now we need to find what is the highest common factor
14:52of two consecutive even numbers we have to find the consecutive even number
14:58let's say two which is the even number after two four six eight ten and it goes
15:05like this we are talking about B part what are the factors of two one and two
15:12factors of four one two and four we are talking about the highest common factor
15:21common factor if I talk about common factors of two and four you can see
15:28here one is common and two is also common so these two have two common
15:35factors one and two which is greater out of these two it is two so highest common
15:42factor of any two consecutive even numbers is two let me take another
15:49combination let us find all the factors of eight I am picking this pair so that
15:55you can understand it goes true for any combination of two consecutive even
16:00number factors of eight one two four and eight these are the factors now highest
16:10common factors of ten one two five and ten these are the highest common factor
16:19which factors are common in both have a look one and one it's common two and two
16:28it's common any other number which is common we cannot find so till now we
16:33have got two common factors one and two we are looking for the highest common
16:39factor what is the greatest number out of these it is two only so highest
16:44common factor here is two for any two consecutive number a part it is one for
16:51consecutive even numbers it is two let us check for consecutive odd numbers
16:57consecutive odd number mean odd number which comes one after the other in the
17:03series let's take the series of odd numbers 1 3 5 7 9 11 13 and so on let us
17:16pick any 2 if I pick 5 and 7 what are the factors of 5 1 and 5 it's being a
17:24prime number factors of 7 1 and 7 again it's a prime number which number is
17:30common in both only one so what is highest common factor that is one let us
17:37take the combination of these two factors of 9 are 1 3 & 9 factors of 11
17:45are 1 & 11 again which factor is common in both it is just one so what is the
17:52highest common factor of any two consecutive odd numbers it is always one
17:58for consecutive numbers is one consecutive odd numbers is also one but
18:04for consecutive even numbers it is two good to go let's move to the next
18:09question now question number three now says the highest common factor of 4
18:16prime number 4 prime numbers are the numbers which do not have any factor in
18:21common between them except one so we have a pair of 4 prime numbers 4 & 15
18:27the factors of 4 2 & 2 factors of 15 3 & 5 I can see here there is no common
18:35prime factor which be common a so can I say that highest common factor is zero
18:40is this the correct answer I told you earlier also if nothing is
18:46common one is always common we do not mention one here it is the prime
18:52factorization one is not a prime number that is why it is not shown here so what
18:59is the highest common factor of any two 4 prime number it is always one it
19:04cannot be zero because one is the factor of every number that is the answer for
19:10question number three I am writing a question here I request you to kindly
19:16find the highest common factors of these number and please put in the
19:20comment option I wait for your answer so your question is find the highest
19:26common factor of 15 45 and 75 that is your question three numbers are being
19:37given 15 45 and 75 you need to give me the highest common factor of these three
19:43numbers I hope you have understood and enjoyed today's session please like and
19:49subscribe my channel for more such informative videos thank you so much for
19:53watching happy learning