Madam, your champs were fast asleep while you were in distress. Please accept my apologies.

 

See, any number N can be uniquely factorised into its prime factors as

 

N = x₁^p x₂^q x₃^r ....

 

Any factor of N can now be constituted as  x₁^p₁ x₂^q₁ x₃^r₁ .... where p₁p,  q₁q,  r₁r

 

Another way is to say, that every factor of N is a term in the following expression:

 

(1+x₁+x₁²+...+x₁^p) (1+x₂+x₂²+...+x₂^q) (1+x₃+x₃²+...+x₃^r)....

Since every factor of N gets listed out, this expression is also the sum of all the factors of N, which is what is shown in your text book.

 

This can be simplified easily using GP summation formula as