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Large Language Models (LLMs) generate fluent long-form text, however, often add unsupported factual claims. Existing verification techniques improve factuality by grounding generation in external evidence. However, the same verification policy usually applies to all claims despite being differences in hallucination risks. We propose \textit{FACTOR} (\textit{FACTuality-Oriented Risk-aware Verification}), an inference-time model that adapts verification criteria according to claim-level uncertainty. FACTOR combines uncertainty estimation, adaptive language inference verification, and candidate re-ranking to allocate verification effort where it is most needed. We evaluate \textit{FACTOR} on FactScore benchmark showing that adaptive verification improves factuality while reducing verification cost simultaneously. We further perform different ablation studies to identify the primary driver of these gains. Our results show the effective and model-agnostic performance of \textit{FACTOR} for improving factuality in long-form generation.