Examples: Tests for Divisibility Video Lecture | Advance Learner Course: Mathematics (Maths) Class 5

hello friends this video on playing with
numbers 523 is brought to you by exam
feel calm no more fear from exam so let
us now quickly look at some of the
questions based on the divisibility
tests right the smallest digit and the
greatest digit in the blank space so
that the number formed is divisible by 3
now what happened what have we learned
from the divisibility test of 3 a number
is divisible by 3 when sum of the digits
is a multiple of 3 or when sum of the
digits is divisible by 3 so for this
number to be divisible by 3 the sum of
its digits so sum of the digits for this
number 4 plus 7 plus 6 plus 5 plus what
is this let us say that the blank space
is X plus X plus 2 so we have to
basically find out the value of x so
this is equal to 24
that is seven folks have four plus seven
plus six plus five plus two that is 24
plus X so this is the sum of the digits
now the question is this sum of the
digits if this is divisible by three
only then this number will be divisible
by three that is our divisibility rule
of three now
what is the smallest number so honest
value that X can take such that 24 plus
X is divisible by three now is 24
divisible by three yes it is three aids
or 24 24 is divisible by three so the
smallest value that X can take is
smallest value of x would be 0 because
when X is equal to 0 this is 24 which is
divisible by 3
and what is the greatest value that X
can take now X is a digit so X can only
be a single digit number so what is the
greatest value of a single digit number
that X can take now think about
because it has to be divisible by 3 now
24 is divisible by 3 now if you add now
if you look at the multiples of 3
quickly look at them by difference of 3
so what are the multiples of 3 the
multiples of 3 goes something like this
three ones are 3 produces 6 3 3 and 9 3
4 12 3 fives of 15 and so on so when you
look at it the smallest value of X could
be 0 and the next value of X could be 3
because if X is 3 then this becomes 27
so 27 is again divisible by 3 the next
value of x could be 6 the next value of
x could be 9 so X can only take these
values because only when X takes these
values this sum will be divisible by 3
right that is quite obvious because if
you add 2 to 24 it becomes 26 26 is not
divisible by 3
now since 24 is already divisible by 3
so in order to make 24 plus X divisible
by 3 X has to be something which is
divisible by 3
so basically X has to be a multiple of 3
so the minimum value that X can take is
0 because when you put X as 0 the sum
remains 24 which is divisible by 3 and
the greatest value that X can take would
be 9 because beyond 9 you have 12 so 12
is a two-digit number but we have space
only for one digit so the maximum value
of x would be 9 so these are the
smallest and the greatest digit possible
in this blank space question number two
using the visibility tests determine if
21,000 eighty-four is divisible by four
by eight so how do we determine if a
number is divisible by four or not
now the divisibility tests of 4 focuses
on the last two digits if last two
digits are degrees
by four then this entire number will be
divisible by four so let us see if the
last two digit is divisible by four or
not so we get a remainder of zero so
that means the last two digits are
divisible by four so therefore we say
that this number is divisible by four
what about eight now to check the
divisibility of eight we have to see if
the last three digits are divisible by 8
or not
so last three digits is zero eight four
which also means 84 because zero at the
beginning has no value so zero eight
four is basically 84 and when you divide
it by eight what do you get so you
basically get a remainder as four that
means 84 is not divisible by 8 therefore
this number as a whole is also not
divisible by eight question number three
using the visibility test determine if
12,500 83 is divisible by six or not now
what does the rule the rule says that if
a number is divisible by both 2 & 3 then
the number is divisible by 6 so now let
us check the divisibility by 2 so is
this number divisible by 2 so in order
to be divisible by 2 the units please
digit has to be 0 2 4 6 or 8 which is
not true in this case therefore this
number is not divisible by 2 now since
this number is not divisible by 2 there
is no point taking its divisibility by 3
because 4 in order to be divisible by 6
it has to be divisible by both 2 & 3 so
therefore we can directly say that the
number will not be divisible by 6
question number 4 right a digit in the
blank space so that the number formed is
divisible by 11 so let us assume that
the digit in the black
spaces X so we have just assumed that
now what do we know as for the rule of
divisibility by eleven now in for a
number would be divisible by 11
only when the difference between the sum
of the digits at odd places and some of
the digits at even places is either zero
or a multiple of 11 so let us first find
out the position of the digits so 1 2 3
4 5 & 6 so these are the odd positions
so some of the digits in the odd places
would be X 4 & 4 so X plus 4 plus 4 that
would be equal to X plus 8 the similarly
some of the digits at even places that
would be equal to these positions 6 4 &
2 that is it would be 8 9 & 8 so 8 plus
9 plus 8 so this would be 25 now let us
try to find out their difference so the
difference would be 25 minus X plus 8 so
this would be 25 minus X minus 8 that is
equal to 17 minus X so this is the
difference now what do we know what know
as per rule that if this difference is
either 0 or it is divisible by 11
only then the number will be divisible
by 11 so let us assume the first case
that if we say that this is equal to 0
so in that case if we say that if 70
minus X is equal to 0 in that case what
would be the value of x the value of x
would be 17 correct but in this case X
is a single digit number so this is not
possible because x
to be a single-digit number because X is
a single digit so that means that this
has to be a multiple of 11 so after zero
what could be the next multiple of 11 so
the next thing that could be is 70 minus
X can be equal to 11 so this means X
will be equal to 17 minus 11 which is
equal to 6 so 6 would be the answer so 6
would be the value of X thank you please
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