Factors Advanced- Under One Minute Video Lecture - Banking Exams

hello students today we are here to
discuss a topic which is favorite of
exam setters of comparative exams like
cat zap etc the topic is number system
students this topic consists of
approximately 20% of the most
competitive exams there are few typical
questions which I will be discussing
with you today by knowing some shortcuts
and techniques you will be able to
easily master this area in your exams so
let us have a look at such question
question is find the sum of perimeters
of all the distinct rectangles with
integral sides whose area is 784 square
units so what is your conventional
approach that is the normal approach
first of all you will take 784 since 784
can be written as 1 into 784 it means
this is a possible rectangle that is a
link to B then you will write down the
second possibility that is 2 into 392
and so on there are numerous cases you
will write down all the possible cases
then you will take sum of all the
parameters if we have a rectangle whose
area is L into B what is very-- meters
formula that is twice of L plus B so by
applying this formula you will calculate
this stuff and in the end you will get
this answer 3 5 9 0 that is a huge huge
approach so do we have any shortcut
method to solve this yes we do have so
let us see a formula by using which will
find some of parameters in lesser time
if you have a number N and if we write
the prime factorization of that number
say it be P raised to power a into Q
raise to power B into R raise to power C
what is sum of factors formula it will
be P raise to power a plus 1 minus 1
upon P minus 1 into Q raise to power P
plus 1 minus 1 upon Q minus 1 into R
raise to power c plus 1
is one upon R - money so on so we will
make use of this formula what was the
area given it was 784 so if we write a
possible rectangle then integral sides
that is 1 into 784 what is a parameter
near that is twice off 1 plus 784 if we
write down one more rectangle let it be
28 into 28 what will be the perimeter
here that will be twice of 28 us 28
so what is the required sum in this case
sum will be nothing but twice of sum of
all the factors since 784 that can be
written as 2 raised to power 4 into 7
square now the formula time apply that
formula that we twice off 2 raised to
power 5 minus 1 upon 2 minus 1 into 7
cubed minus 1 upon 7 minus 1 plus now
that was the catch twice into 28 why are
we adding 28 twice in the total sum
because we are considering this
rectangle where both the sides are 28
and 28 of course square is also a
rectangle so there is a factor 28 which
we have counted twice corresponding to
that we are taking twice of 28 now if
you solve this sum you will get answer
is 3 5 9 0 square units I hope the idea
is clear now you see the full length
video log on to hit bull's eye calm
thank you so much