In how many ways can 73920 can be factorised into 2 co prime factors?

73920 = $$2^6 * 3 * 5 * 7 * 11$$

There are 5 prime factors: These should be distributed among 2 variables. If all 5 prime factors go to one variable, number of ways of distribution = 1
If 4 prime factors go to one variable and the fifth one to the other: No. of ways of distribution = 5C4 = 5 ways
If 3 prime factors go to one variable and the other two to the other variable: No. of ways of distribution = 5C3 = 10 ways
The other combinations are just repetitions of the above combinations.

So, no. of ways in which 73920 can be factorised into 2 co-prime factors is 1 + 5 + 10 = 16 ways