I just didn't realize it... but heres the gist of my way thats basically the same as CPHILL I didn't get it at first because instead of 3^2 I thought it was 32...
The prime factorization of 144000 is2^7*3^2*5^3 , so the minimum sum in this case is 35 .
Thanks Melody and Cphill and mathhemath and waffles!