Step 1: Frame the competition of forces. Inside a nucleus two influences compete: the long-range Coulomb repulsion among the positively charged protons, and the strong but short-range nuclear attraction between every pair of nucleons. Neutrons are electrically neutral, so adding them boosts the binding attraction while adding no repulsion.
Step 2: Identify the controlling quantity. Because the number of neutrons decides how much extra binding is available to counter proton repulsion, the key parameter is how many neutrons accompany each proton, that is the \(N/Z\) ratio. Too few neutrons and Coulomb repulsion dominates; too many and the nucleus is neutron-rich and again unstable.
Step 3: Conclusion. Thus nuclear stability is governed chiefly by the neutron-proton ratio.
\[\boxed{\text{Chief factor} = \dfrac{\text{number of neutrons}}{\text{number of protons}}\ (N/Z)}\]