Use Exercise 27 to determine the number of abelian groups (up to isomorphism) of order (10)⁵.

Data from exercise 27

Following the idea suggested in Exercise 26, let m and n be relatively prime positive integers. Show that if there are (up to isomorphism) r abelian groups of order m ands of order n, then there are (up to isomorphism) r s abelian groups of order mn.