Objective: To assess the effect of operational factors on the positivity rates of three HPV assays. Methods: Within the cross‐sectional ESTAMPA study, women aged 30–64 years were recruited at healthcare centers from Soacha, Colombia, during 2012–2015. Cervical samples were collected for cotesting with Hybrid Capture 2 (HC2; Qiagen, Gaithersburg, MD, USA), and either Aptima (Hologic, Marlborough, MA, USA) or Cobas 4800 (Roche Diagnostics, Indianapolis, IN, USA). The effect of operational factors on assay performance was assessed using adjusted positivity rates obtained from logistic regression models. Results: There were 4168 women included. For samples collected in assay‐specific medium, positivity rate differences were associated with the expertise of the nurse collecting the sample (P=0.014 HC2; P=0.091 Aptima) and if sample collection occurred after an initial cytology (P=0.025 HC2; P=0.033 Aptima). If PreservCyt medium (Hologic) was used, HC2 positivity differences were observed depending on the time between sample collection and processing (P=0.026) and on the laboratory technician processing the samples (P=0.003). No differences were observed for PreservCyt samples processed with Aptima or Cobas. Conclusion: Nurse expertise, collection of previous cytology, processing time, and laboratory technician could influence HPV assay performance. Suitable quality assurance protocols for HPV‐based screening programs are required.