  Finding the factors of an integer can be achieved by various experimental
techniques, based on an algorithm developed by Schleich et al., which uses
specific properties of Gau\ss{}sums. Experimental limitations usually require
truncation of these series, but if the truncation parameter is too small, it is
no longer possible to distinguish between factors and so-called "ghost"
factors. Here, we discuss two techniques for distinguishing between true
factors and ghost factors while keeping the number of terms in the sum constant
or only slowly increasing. We experimentally test these modified algorithms in
a nuclear spin system, using NMR.
