Allow me to build upon what Tkh has given you. Although I am generally opposed to working out problems, having taught this a number of times I find students always have trouble with it.
Because 55125 = 32·53·72 then any factor of 55125 must be of the form 3a·5b·7c where 0 £ a £ 2, 0 £ b £ 3, and 0 £ c £ 2.. In essence we need to count the number of triples (a,b,c) that satisfy those conditions. For (0,0,0) we get the factor 1, for (2,3,2) we get the factor 55125.
I will tell the end result is 36. How did we get this number?