L15 : Divisibility by 4 - Playing With Numbers , Maths, Class 6 Video Lecture

hello friends this video on playing with
numbers 515 is brought to you by exam
feel calm no more fear from exam let us
now learn about the divisibility by 4
rule so how do we know a number is
divisible by 4 so a number is divisible
by 4 if the number formed by its last
two digits is divisible by 4 so in this
case again you do not need to focus on
the length of the number doesn't matter
how big the number is you just need to
focus on the last two digits so for
example you have a number 492 so you
really do not need to bother about the
entire number just focus on the last two
digits that is the digit as the units
please and the digit at the 10 space so
all together this is 92 so now you have
to check by actual division if 92 is
divisible by 4 or not and that is pretty
simple so if you actually check this
what do you see you see that 92 is
divisible by 4 and therefore this entire
number would be the musical bye for now
this is more advantageous for bigger
numbers for example let's say you have a
number like this 3 4 1 2 0 8 and if I
ask you if this number is divisible by 4
or not it is tough to divide such a big
number by 4 so you just look at the last
two digits which is 8 and which is
clearly divisible by 4 therefore the
entire number is also divisible by 4 so
here again you might be curious to know
how this rule works that why do we need
to verify the last two digits if they
are divisible by 4 so let's take the
same number which is 3 4 1 2 0 8 so the
first thing that we will do in this case
also is we will expand the number so
this is at units place tens hundreds
thousands ten thousands and lakhs so 3
into 10 to the power one two
three four five plus four into 10,000
plus one in two thousand plus 2 into 100
plus 0 into 10 plus 8 into 1 this is how
you will expand the numbers now what we
do now here in like in case of 3 what we
did we wrote thousand as 999 plus 1
because 999 was divisible by 3 but in
this case we want to check the
divisibility by 4 so we will follow a
different trick so here what is the
trick that we are going to follow now
looking at these numbers we have to
decide that how these numbers are going
to help us to find its divisibility by 4
now if you look at it you see that is 10
divisible by 4
ten is not divisible by 4 right because
when you write the multiples of 4 it
would be something like 4 then 8 and
then 12 and so on so 10 is not divisible
by 4 but what about hundred is 100
divisible by 4 let us quickly do an
actual division to see if 100 is
divisible by 4 and go to we see we see
that hundred is divisible by 4 now since
hundred is divisible by 4 that means any
multiple of 100 would also be divisible
by 4
therefore multiple of hundred is also
divisible by 4 so that means if hundred
is divisible by 4 then 100 into 10 that
is thousand is also divisible by 4 then
100 in 200 that is 10
thousand is also divisible by four then
100 multiplied by anything will also be
divisible by four okay
so that means when you look at these
terms what do you see so with this you
will see that this term is divisible by
four why because this term is basically
a multiple of 100 what about this term
this term is also divisible by four this
term contains thousand so it is also
divisible by four
this has hundred so this is also
divisible by four so what are we left
with we are left with these two terms so
basically what are we left with we are
left with 0 into 10 plus 8 into 1 that
means the digit act the unit's place and
the digit at the tens place so we are
basically left with these two digits and
that is what we are doing what we are
saying is if the number formed by the
last two digits is divisible by 4
because these last two digits are the
ones which we are unsure of which we are
not sure our doubt is only that whether
the last two digits are divisible by 4
or not because the remaining digits
I always divisible by 4 so the doubt
lies only with the last two digits that
is why we have made this rule like this
so let us quickly look at these numbers
and see if these are divisible by 4 so
the first number is 2 4 5 6 so we will
focus only on the last two digits that
is 56 now by quick division we will see
if 56 is divisible by 4 so this is 4 1
so 4 and then 4 4 16 so 56 is divisible
by 4 therefore this entire number is
divisible by 4 look at this number this
is such a huge number now if this number
can actually scare you if somebody asks
you to quickly tell if this is divisive
before or not but with this divisibility
rule it will not scare you because you
need to bother only about the last two
digits which is 61 and it is pretty
simple to actually divide and see if 61
is divisible by 4 or not now in this
case what do you see you have a reminder
so that means 61 is not divisible by 4
and therefore this number as a whole is
not divisible by 4 let's look at a third
number so this is also like a nine digit
number so let's focus on the last two
digits which is 44 and 44 is divisible
by 4 because 44 is nothing but 4 into 11
so it is divisible by 4 therefore this
entire number is also divisible by 4
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