Some Important Points related to Factors and Multiples Video Lecture -

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based on whatever we have studied so far
on factors and multiples let us see what
did we conclude because there are
certain important things that we knew
about factors and multiples now a factor
has to be an exact divisor of the number
only then it becomes a factor of that
number so you think of any example so
let's let's think of this example 4 so
who would be a multiple of four only
that number which divides four exactly
leaving zero as remainder for example
one would be an exacta bezel two would
be an exactly sir for itself would be an
exact division so one two and four would
be the factors of number four one is the
factor of every number now if you want
you can just observe it for yourself so
it is T four so what are the factors of
four 4 can be written as 1 into 4 it can
be written as 2 into 2 it can be written
as 4 into 1 now when we write 4 as 2
into 2 it basically means that 2 exactly
divides 4 where to the other two would
be quotient and the remainder would be 0
similarly when you divide 4 by 4 the
quotient would be 1 and the remainder
would be 0 so considering these we find
that 1 2 & 4 are factors of 4 similarly
think of a number like 8 so 8 can be
written as 1 into H 2 into 4 4 into 2 8
into 1 so basically looking at these you
can say 1 2 4 8 are the factors of 8 now
did you notice something that one is
common for both of them
in fact you consider any number occurred
see the 13 you consider 50
you consider hundred everywhere you
would see that one is a factor because
one divides every number every number is
a factor of itself now that is also
another interesting fact that four is a
factor of four eight is a factor of
eight thirteen is a factor of 13 59 is a
factor of 59 and so on so basically one
and the number itself these two factors
will be there for every number a factor
is always less than or equal to the
number so that is also very much evident
because who would be a factor and exact
division so that exact division has to
be less than the number itself or as the
math can be equal to the number so you
see four four if the factors are even
less than four like one and two or equal
to four
similarly for eight the factors are
either less than eight like one two and
four or it is equal to eight a number
has finite number of factors finite
means fixed number of or limited number
of factors so if you consider this
number four so how many factors number
four has one two and four so basically
it has three factors you think of number
eight how many factors it has one two
three four so it has four factors and
these number of factors remain constant
so four cannot have more than three
factors these are the only possible
factors or four so for every number you
have a finite number of factors now when
we come to the multiples we see that
every one every number is a multiple of
itself but that is one very interesting
fact that every number is a factor of
itself and every number is also a
multiple of itself now let us look at an
example let us consider the number four
and let us try to write its multiples so
these would be the multiples of four so
basically what do you see that the
multiples star
with the number itself so if it is for
four when multiplied by one is for
itself and that is which which property
of whole number is this can you recall
from the previous lesson it is nothing
but multiplicative identity one is
called the multiplicative identity
because when you multiply one to any
number the number remains the same and
that is the reason while four is a
multiple of itself because four when
multiplied by one gives the number
itself that is it gives for a multiple
is always more than or equal to the
number so that's another interesting
thing because when we were talking about
factors we were actually trying to
divide the number by their factors but
when we talk about multiples we try to
multiply the number so you see in order
to find the multiples what are we doing
we are multiplying the number four by
one two three four five and so on but
when we were trying to find factors of
whole what were we trying to do we were
trying to divide 4 by 1 2 3 4 and so on
and then try to find out where the
remainder is zero so since here we are
multiplying so it is quite obvious that
the value of the multiples would be more
than that of the number or at least it
would be equal to the number so a
multiple will always be more than or
equal to the number a number has
infinite number of multiples as you can
see here that these the count of these
natural numbers starting from 1 2 3 4 5
and so on
this would continue to infinity so you
might reach a number where you actually
trying to multiply 4 by infinity so what
would you get you would get infinity so
basically the number of multiples are
also in finite so you can start from 4a
12 16 20 24 28 so you can go on and on
and you would write in finite number of
multiples of four not only Ford this is
true for any number so these are some of
the differences between factors and
multiples so I hope that the concept of
factors and multiples are absolutely
clear now if it is not clear please
replay and watch the video again but get
your concept clear thank you please
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