In the era of the Internet of Things (IoT), remote sensors and endpoint appliances generate vast amounts of data. Decentralized and collaborative learning builds on these IoT data to enable classification and recognition tasks by inviting multiple data owners. Federated learning (FL), as a popular collaborative learning framework, can significantly improve the performance of models without collecting the original data. To invite data owners to participate in FL, various incentive mechanisms are designed to address this issue by researchers. However, existing solutions still face high costs and low utility due to information asymmetry, where the reputation, computation power, and data quantity of the data owners are not known in advance. Therefore, we propose a Stackelberg Game-Based Multi-Factor Incentive Mechanism for Federated Learning (SGMFIFL). First, we design the Top-K cost selection algorithm based on reverse auction, which can reduce the cost of selecting data owners. Next, we devise a multi-factor reward function based on reputation, accuracy, and reward rate, the data owners with high reputation and high accuracy will be of more reward. In particular, to ensure that SGMFIFL can provide reliable incentives in IoT, we use blockchain to provide a secure and trusted environment. Finally, we construct a two-stage Stackelberg game model for the task publisher and the data owners and derive an optimal Equilibrium solution for both stages of the whole game. Experiments conducted on two well-known datasets, MNIST and CIFAR10, demonstrate the significant performance of the proposed mechanism.