The sum of all divisors of 2⁵.3⁴.5² is

the rite answer i guess shud be b)....

there is an expression for the sum of all factors of p₁^ap₂^bp₃^c........where p1, p2 , p3 are prime numbers....

which is (p₁^a+1-1)/(p₁-1) * (p₂^b+1-1)/(p₂-1)*...........

so applying this u get the above result..........

rate if useful........

this cud be proved in the following manner........

p₁^ap₂^bp₃^c

the factors of this exp contain various combinations of the powers of each prime no. from 0 to the power(ie a,b etc)

so the sum of factors cud be expressed as (1+ p₁+p₁²+p₁³.......p₁^a)*(1+ p₂+p₂²+p₂³.......p₂^b)*......

= (p₁^a+1-1)/(p₁-1) * (p₂^b+1-1)/(p₂-1)*...........

a very useful expression.......

rate if useful........

The answer for the question is the 2nd option.



To find the sum of divisors of a number first we have to do prime factorization and then we have to write it in powers of primes then use the formula



((P1^(n+1)-1)/P1-1)((P2^(n+1)-1)/P2-1)......................

You will understand it better with an example:

Finding the sum of factors of 720

Now coming to the problem there is no need to factorize it as it is in powers of primes, therefore we will directly apply the formula

((2^(5+1)-1)/2-1)x((3^(4+1)-1)/3-1)x((5^(3+1-1))/5-1)

=63x121x31=3^(2)x7^(1)x11^(2)x31^(1)

Therefore the answer is the 2nd option