Writing Numbers as a Product of Powers of Prime Factors Video Lecture - Class 7

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let us see how can we represent a number
as a product of powers of prime factors
like how I mean if we alanda be given
any number so how do we write it in in
the form of powers now before even
before we write a number like this let
us understand what do we mean by writing
as a product of powers so here this
little boy gives us a number
can you write 144 as a product of powers
of prime factors now let us understand
what do we mean by writing as product of
powers that means we have to write this
number 144 in this form where you have a
prime factor now by now you all know
what is a prime factor that factor which
cannot be factorized for them so we will
see you remember the prime factorization
method by which we find out the prime
factors of any number that is those
factors which are not only factors but
also prime numbers they are called prime
factors in case you have forgotten it
please refer to the existing video of
prime factorization okay so how we have
to represent it is you have a prime
factor and then this prime factor to the
power some number again multiplied by
some other prime factor to the power
some number B so a prime factor to the
power a multiplied by a prime factor to
the power B multiplied by a prime factor
to the power C so something in this
pattern so something in this form so
what is happening so you see these are
powers right this is exponential form
this is exponential form and this is
product of powers so that is why it is
called a representing a number has
product of powers of prime factors now
let us see how we do this so in order to
do this like this is our given number
144 so the first step to do this is to
do prime factorization of 144 so how do
we do private
of 144 so we liked 144 which is the
smallest possible right number that's
two so we divided by tools only if it is
completely divisible by two so in this
case it is so two sevens of fourteen to
two so for now this again is divisible
by 2 so 2 3 is a 6 2 6 is 12
again this is divisible by 2 services to
ones or 2 2 8 to 16 now also it is
divisible by 2 because two nines are 18
now is nine divisible by two
no so which is the next prime number
that's 3 is it divisible by 3 yes so 3
into 3 is 9 so now if we want to write
this number 144 as a product of the
prime factors how can we write this 144
is equal to 2 into 2 into 2 into 2 into
3 into 3 so basically you multiply all
of these you get the number 144 so when
you look at it what happens here so 2 is
getting multiplied for 4 times so how
can we write this in exponential form we
can write it as 2 to the power 4
similarly when you look at 3 3 is
getting repeated two times so this is 3
to the power 2 so basically 144 can be
written as product of powers of prime
factors 2 & 3 are prime factors 4 & 2
are their respective powers and this 144
is the product of the two so this is
what we mean by representing a number as
a product of powers of time thank you
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