Class 6 Exam > Class 6 Videos > Examples: Highest common factor(HCF)
Examples: Highest common factor(HCF) Video Lecture - Class 6
FAQs on Examples: Highest common factor(HCF) Video Lecture - Class 6
| 1. What is the highest common factor (HCF) and how is it calculated? |  |
Ans. The highest common factor (HCF) is the largest positive integer that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD). To find the HCF, we can use methods like prime factorization or the division method.
| 2. How can I find the HCF using prime factorization? | |
Ans. To find the HCF using prime factorization, we need to express all the given numbers as a product of prime factors. Then, the HCF is obtained by taking the product of the common prime factors with the lowest exponent.
| 3. Can the HCF of two numbers be greater than the smaller number? | |
Ans. No, the HCF of two numbers cannot be greater than the smaller number. The HCF is always a factor of both numbers, so it must be less than or equal to the smaller number.
| 4. Are there any shortcuts or tricks to find the HCF quickly? | |
Ans. Yes, there are a few shortcuts to find the HCF quickly. One such method is the division method, where we divide the larger number by the smaller number and continue dividing the remainder by the previous divisor until we get a remainder of zero. The last divisor used will be the HCF.
| 5. Can the HCF of three or more numbers be zero? | |
Ans. No, the HCF of three or more numbers cannot be zero. The HCF is always a positive integer, as it represents the largest common factor among the given numbers. If all the numbers are zero, then the HCF would also be zero, but in any other case, the HCF will always be greater than zero.
Text Transcript from Video
hello friends this video on playing with
numbers part 31 is brought to you by
exam feel calm no more for your exam
pebble so let us quickly look at some of
the questions based on HCF find the HCF
of 34 and 102 so we will find it out by
prime factorization method so 217 34 17
is a prime number so 17 into 1 so 34 can
be written as 2 into 70 now let us do
prime factorization of 102 so this would
be 2 fives a 10 to 1 z 2 this would be 3
1 2 3 3 7 21 so this would be 17 into 1
so 102 can be written as 2 into 3 into
17
now let us mark the common that we have
2 is common here 2 is also common here
17 is present here 17 is also present
here so 2 and 17 these are the common
things now can you tell me what would be
the HCL so even though I can't hear you
but please tell it by yourself so that
you will get to understand it so that
you learn it so what would be the HCF
now 2 is also common in both 17 is also
common in both so we know the common
factors but I want to find the highest
common factor so what we will do we will
multiply the common factors that is 2
into 17 this entire package is common in
both so basically the HCF of 34 and 102
is 34 find the HCM of 12 45 and 75 so
you can even find it CF between 3
numbers this is going to be interesting
so let's do prime factorization of 12 so
2 sixes are 12 2 3 is 6 and then 3 1 2 3
so 12 can be written as 2 into 2 into 3
let's do it for 45 so this would be we
believe divided by 3 3 1 2 3 3 types of
15 again 3 5 so 15 and then 5 months
five so 45 can be written as 3 into 3
into 5 the third one is 75 so this would
again not by 3 but this would be
divisible by five so five ones a file
and the five fights are 25 again 5 3 15
then 3 ones of 3 so 75 can be written as
5 into 5 into 3 so this is how we have
done the prime factorizations now let us
try to find out the common thing now
here when we find something common that
means that the number should be present
in all of them so to do you think 2 is a
common factor for all of them no what
about 3 so 3 exists here 3 also exists
here and 3 also exists here so 3 is one
common factor so what is the other
common factor 2 is not a common factor
because it is not present in both of
them 5 5 is present 5 is a factor of 45
5 is also a factor of 75 but 5 is not a
factor of 12 so what would be the HCF
because here the only common factor is 3
so the HCF of 12 45 and 75 would be 3
now if you want to verify the HCF using
the alternative method that is using the
same method of factors you can even do
that and you will arrive at the same
result so if you want to try you can
give it a try but again you will arrive
at the same result question number 3
find the HCF of 91 112 and 49 find the
HCF of 91 112 and 49 see here also we
will do the same procedure that is we
will first do prime factorization of
each of these numbers so let us start
with 91 so 7 is the smallest prime
number by which it is completely
divisible so this would be third
and this would be like 13 into one so 91
can be written as 7 into 13 next is 112
so two fives are 10 to 60 12 to 2 so 4
2016 2 1 z 2 2 4 z 8 2 7 is a 14 7 1 7
so 112 can be written as 2 into 2 into 2
into 2 into 7 the third number that is
49 this can be written as 7 into 7 and
then 7 & 2 1 & 7 so 49 can be written as
7 into 7 so let us find out the common
factors so 7 is a common factor because
it is present in all of them other than
that do you have any common factors No
therefore HCF of 91 112 and 49 is 7
question number 4 what is the HCF of two
consecutive numbers so you think of any
two consecutive numbers what would be
the HCL so let us take examples and then
see the results so let us talk about two
numbers like 4 & 5 so what would be the
HCF of 4 & 5
so do you want to try so let us let us
try this the 4 can be written as so or
we can say if there are 2 different ways
of doing it one way is 4 can be written
as 2 into 2 5 can be written as 5 into 1
now when you write 2 into 2 you
explicitly you actually mean 2 into 2
into 1 so which is the common factor
that you have so 1 is the common factor
therefore HCF will be equal to 1 so even
if you do it by the other process let us
talk about 4 so what are the factors of
4 1 2 & 4 what are the factors of 5 1 &
5 so which is a common factor 1 so which
is the highest common factor it is 1 so
by both the methods you see that it's
of two consecutive numbers whether it is
for fight whether it is 15:16 or it is
9900 for any two consecutive numbers
there HCF will always be one let's talk
about two consecutive even numbers so
what do we mean by two consecutive even
numbers for example if one number is
four the other number would be six even
numbers are those numbers which are
divisible by 2 so 4 & 6 so let us look
at it so what are the factors of 4 1 2 4
what are the factors of 6 1 2 3 6 so
what is the HCF so here this is a common
factor 1 another common factor is 2 so
which is the highest common factor
definitely to let us look at some other
examples take one more example let's
consider 24 and 26
so for 24 what are the factors 1 2 3 4 6
8 12 and 24 these are the factors for 24
for 26 the factors would be 1 to 13 and
26 so here also you see 1 is a common
factor and 2 is another common factor so
the highest common factor by this method
also is 2 if you want you can find out
try to find out the hc8 using prime
factorization method there also you get
the same result so when you talk about
HCF of two consecutive even numbers like
4 6 24 26 28 30 2 4 so for any two
conjugative even numbers the 18th will
always be 2 now the third one that is
two consecutive odd numbers now let's
consider two consecutive odd numbers for
example 3 & 5
now when you try to write the factors of
3 you get 1 & 3 4 5 you get 1 and find
so common factor is 1 therefore HCF
would be 1 similarly if you take example
of one hundred
and 103 these are two consecutive odd
numbers that is numbers which are not
divisible by 2 so 101 factors would be 1
and 1 0 and 103 factors would be 1 and 1
0 3 so here also the HCF would be 1 in
fact you will try it out with any other
set of odd numbers but they should be
consecutive like 5 7 like seven nine
nine eleven so any of these pairs if you
try to find out it HCF the h-scenes will
come out to be one question number five
atf of co-prime numbers four and fifteen
was found as follows by factorization 4
is equal to 2 into 2 and 15 is equal to
3 into 5 since there is no common factor
there is no common prime factor so HCF
of 4 and 15 is zero is the answer
correct absolutely not because when we
write 2 into 2 there is basically a 1
hidden here which we do not write
because my define anything by 1 will
give the number itself so basically
there is a 1 which is being hidden here
so 1 is always a common factor between
any two numbers doesn't matter whichever
numbers they are whether they are odd or
even they're consecutive or
non-consecutive for any two numbers you
will always have 1 as a common factor
one will always be there no other than 1
you might have many more common factors
but one will be there so in this case
the HCF will not be equal to 0 but it
would be equal to 1
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numbers part 31 is brought to you by
exam feel calm no more for your exam
pebble so let us quickly look at some of
the questions based on HCF find the HCF
of 34 and 102 so we will find it out by
prime factorization method so 217 34 17
is a prime number so 17 into 1 so 34 can
be written as 2 into 70 now let us do
prime factorization of 102 so this would
be 2 fives a 10 to 1 z 2 this would be 3
1 2 3 3 7 21 so this would be 17 into 1
so 102 can be written as 2 into 3 into
17
now let us mark the common that we have
2 is common here 2 is also common here
17 is present here 17 is also present
here so 2 and 17 these are the common
things now can you tell me what would be
the HCL so even though I can't hear you
but please tell it by yourself so that
you will get to understand it so that
you learn it so what would be the HCF
now 2 is also common in both 17 is also
common in both so we know the common
factors but I want to find the highest
common factor so what we will do we will
multiply the common factors that is 2
into 17 this entire package is common in
both so basically the HCF of 34 and 102
is 34 find the HCM of 12 45 and 75 so
you can even find it CF between 3
numbers this is going to be interesting
so let's do prime factorization of 12 so
2 sixes are 12 2 3 is 6 and then 3 1 2 3
so 12 can be written as 2 into 2 into 3
let's do it for 45 so this would be we
believe divided by 3 3 1 2 3 3 types of
15 again 3 5 so 15 and then 5 months
five so 45 can be written as 3 into 3
into 5 the third one is 75 so this would
again not by 3 but this would be
divisible by five so five ones a file
and the five fights are 25 again 5 3 15
then 3 ones of 3 so 75 can be written as
5 into 5 into 3 so this is how we have
done the prime factorizations now let us
try to find out the common thing now
here when we find something common that
means that the number should be present
in all of them so to do you think 2 is a
common factor for all of them no what
about 3 so 3 exists here 3 also exists
here and 3 also exists here so 3 is one
common factor so what is the other
common factor 2 is not a common factor
because it is not present in both of
them 5 5 is present 5 is a factor of 45
5 is also a factor of 75 but 5 is not a
factor of 12 so what would be the HCF
because here the only common factor is 3
so the HCF of 12 45 and 75 would be 3
now if you want to verify the HCF using
the alternative method that is using the
same method of factors you can even do
that and you will arrive at the same
result so if you want to try you can
give it a try but again you will arrive
at the same result question number 3
find the HCF of 91 112 and 49 find the
HCF of 91 112 and 49 see here also we
will do the same procedure that is we
will first do prime factorization of
each of these numbers so let us start
with 91 so 7 is the smallest prime
number by which it is completely
divisible so this would be third
and this would be like 13 into one so 91
can be written as 7 into 13 next is 112
so two fives are 10 to 60 12 to 2 so 4
2016 2 1 z 2 2 4 z 8 2 7 is a 14 7 1 7
so 112 can be written as 2 into 2 into 2
into 2 into 7 the third number that is
49 this can be written as 7 into 7 and
then 7 & 2 1 & 7 so 49 can be written as
7 into 7 so let us find out the common
factors so 7 is a common factor because
it is present in all of them other than
that do you have any common factors No
therefore HCF of 91 112 and 49 is 7
question number 4 what is the HCF of two
consecutive numbers so you think of any
two consecutive numbers what would be
the HCL so let us take examples and then
see the results so let us talk about two
numbers like 4 & 5 so what would be the
HCF of 4 & 5
so do you want to try so let us let us
try this the 4 can be written as so or
we can say if there are 2 different ways
of doing it one way is 4 can be written
as 2 into 2 5 can be written as 5 into 1
now when you write 2 into 2 you
explicitly you actually mean 2 into 2
into 1 so which is the common factor
that you have so 1 is the common factor
therefore HCF will be equal to 1 so even
if you do it by the other process let us
talk about 4 so what are the factors of
4 1 2 & 4 what are the factors of 5 1 &
5 so which is a common factor 1 so which
is the highest common factor it is 1 so
by both the methods you see that it's
of two consecutive numbers whether it is
for fight whether it is 15:16 or it is
9900 for any two consecutive numbers
there HCF will always be one let's talk
about two consecutive even numbers so
what do we mean by two consecutive even
numbers for example if one number is
four the other number would be six even
numbers are those numbers which are
divisible by 2 so 4 & 6 so let us look
at it so what are the factors of 4 1 2 4
what are the factors of 6 1 2 3 6 so
what is the HCF so here this is a common
factor 1 another common factor is 2 so
which is the highest common factor
definitely to let us look at some other
examples take one more example let's
consider 24 and 26
so for 24 what are the factors 1 2 3 4 6
8 12 and 24 these are the factors for 24
for 26 the factors would be 1 to 13 and
26 so here also you see 1 is a common
factor and 2 is another common factor so
the highest common factor by this method
also is 2 if you want you can find out
try to find out the hc8 using prime
factorization method there also you get
the same result so when you talk about
HCF of two consecutive even numbers like
4 6 24 26 28 30 2 4 so for any two
conjugative even numbers the 18th will
always be 2 now the third one that is
two consecutive odd numbers now let's
consider two consecutive odd numbers for
example 3 & 5
now when you try to write the factors of
3 you get 1 & 3 4 5 you get 1 and find
so common factor is 1 therefore HCF
would be 1 similarly if you take example
of one hundred
and 103 these are two consecutive odd
numbers that is numbers which are not
divisible by 2 so 101 factors would be 1
and 1 0 and 103 factors would be 1 and 1
0 3 so here also the HCF would be 1 in
fact you will try it out with any other
set of odd numbers but they should be
consecutive like 5 7 like seven nine
nine eleven so any of these pairs if you
try to find out it HCF the h-scenes will
come out to be one question number five
atf of co-prime numbers four and fifteen
was found as follows by factorization 4
is equal to 2 into 2 and 15 is equal to
3 into 5 since there is no common factor
there is no common prime factor so HCF
of 4 and 15 is zero is the answer
correct absolutely not because when we
write 2 into 2 there is basically a 1
hidden here which we do not write
because my define anything by 1 will
give the number itself so basically
there is a 1 which is being hidden here
so 1 is always a common factor between
any two numbers doesn't matter whichever
numbers they are whether they are odd or
even they're consecutive or
non-consecutive for any two numbers you
will always have 1 as a common factor
one will always be there no other than 1
you might have many more common factors
but one will be there so in this case
the HCF will not be equal to 0 but it
would be equal to 1
thank you please visit exam fee or come
for free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
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