In 2022, Yan et al. proposed a new quantum integer factorization algorithm (SQIF: Sublinear-resource Quantum Integer Factorization algorithm) which requires a sublinear number of qubits for factoring an m-bit integer. In contrast, Shor’s quantum algorithm requires a linear number of qubits. SQIF is a combination of Schnorr’s classical factorization algorithm and the quantum approximate optimization algorithm (QAOA). Since QAOA is tolerant to errors that occurred during the process, it is claimed that the proposed algorithm can challenge a 2048-bit integer factorization even on the existing noisy quantum computers. The purpose of this paper is to examine SQIF in detail. Firstly, while SQIF finds only a few relations, we propose a method to find a sufficient number of relations for the factorization by a quantum way. Secondly, this paper shows experimental results for factoring from 11-bit to 55-bit integers by our algorithm using the annealing computer for the optimization. Our results show that a sublinear number of qubits seems to be insufficient and the computational complexity is prohibitive for the optimization-based factorization.