  Several physics-based algorithms for factorizing large number were recently
published. A notable recent one by Schleich et al. uses Gauss sums for
distinguishing between factors and non-factors. We demonstrate two NMR
techniques that evaluate Gauss sums and thus implement their algorithm. The
first one is based on differential excitation of a single spin magnetization by
a cascade of RF pulses. The second method is based on spatial averaging and
selective refocusing of magnetization for Gauss sums corresponding to factors.
All factors of 16637 and 52882363 are successfully obtained.
