How many positive factors are there of the number 360 and find the sum of all these factors.

360 = 6².5.2

360 = 2³.3².5

therefore no of factors = (3+1)(2+1)(1+1) = 24

this  comes as  i can take  2  : none i.e 1 , one two =2 , two two''s (2²)=4 , three two''s(2³) = 8

and same for the other primes also  

sum of all the factors = (2⁰+2¹+2²+2³ )(3⁰+3¹+3²)(5⁰+5¹)

if you see carefully the above expression represents sum of all the factors 

  like      2⁰.3⁰.5⁰ =1 

and     2³.3².5¹ = 360 

now apply individual sum of G.P. formula for the 3 brackets and obtain the answer 

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