Large Language Models (LLMs) frequently generate hallucinated content, posing significant challenges for applications where factuality is crucial. While existing hallucination detection methods typically operate at the sentence level or passage level, we propose FactSelfCheck, a novel zero-resource black-box sampling-based method that enables fine-grained fact-level detection. Our approach represents text as interpretable knowledge graphs consisting of facts in the form of triples, providing clearer insights into content factuality than traditional approaches. Through analyzing factual consistency across multiple LLM responses, we compute fine-grained hallucination scores without requiring external resources or training data. Our evaluation demonstrates that FactSelfCheck performs competitively with leading sentence-level sampling-based methods while providing more detailed and interpretable insights. Most notably, our fact-level approach significantly improves hallucination correction, achieving a 35.5% increase in factual content compared to the baseline, while sentence-level SelfCheckGPT yields only a 10.6% improvement. The granular nature of our detection enables more precise identification and correction of hallucinated content. Additionally, we contribute FavaMultiSamples, a novel dataset that addresses a gap in the field by providing the research community with a second dataset for evaluating sampling-based methods.