Question 990562
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27720 = 8*9*5*7*11


is the presentation of the number  27720  as the product of five co-prime numbers  8, 9, 5, 7, and 11. 


So,  we have basically  5  co-prime numbers,  and the question is:  in how many ways we can collect some of them into the first factor?  (Then the rest of them will 

automatically go into the second factor).  The order of co-primes in the first factor does not make a difference.  (Same as the order in the second factor does not).


It is the same as to ask:  how many sub-sets is there in the set of  5  object? 


The answer is:  {{{2^5}}}.


Indeed,  the empty sub-set corresponds to the value  1  of the first factor.


The sub-sets consisting of  1  elements,  give the values of 8, 9, 5, 7, and 11  for the first factor.


The sub-sets consisting of 2 elements give the factors 8*9, 8*5, 8*7, . . . , 7*11. 


The sub-sets . . . . and so on.


Thus the number of ways in which we can construct the first factor is  {{{2^5}}}. 

But since we do not make the difference between the first and the second factors,  we need to divide this number by  2.


So,  the answer is:  The number of ways in which the number  27720  can be split into the product of two co-prime factors is  {{{2^4}}}.