Verifying fact-checking claims poses a significant challenge, even for humans. Recent approaches have demonstrated that decomposing claims into relevant questions to gather evidence enhances the efficiency of the fact-checking process. In this paper, we provide empirical evidence showing that this question decomposition can be effectively automated. We demonstrate that smaller generative models, fine-tuned for the question generation task using data augmentation from various datasets, outperform large language models by up to 8%. Surprisingly, in some cases, the evidence retrieved using machine-generated questions proves to be significantly more effective for fact-checking than that obtained from human-written questions. We also perform manual evaluation of the decomposed questions to assess the quality of the questions generated.