Looking at two versions of Fundamental Abelian groups theorem 

*

*$G$ is a finite abelian group. Then it can be expressed with a direct product of cylic groups with prime power order


*$G$ is a finite abelian group with order $n$. Then it can be expressed as
$$C_{r1} \times...\times C_{rk}$$
where $r_1 |r_2|...|r_k$ and $r_1r_2...r_k=n$.

The first version gave me $6$ isomorphic cyclic direct products for a abelian group of order $600$. I was aksed of this in a problem.
However, I tried using the second theorem out of curiosity but all I could get is

(600),(2,300),(5,120),(10.60),(2,2,150) as the possible $r_k$s.

Can anyone come up with the last set of factors?

I guess it should be $(2,10,30)$.
