  The task of factoring integers poses a significant challenge in modern
cryptography, and quantum computing holds the potential to efficiently address
this problem compared to classical algorithms. Thus, it is crucial to develop
quantum computing algorithms to address this problem. This study introduces a
quantum approach that utilizes Rydberg atoms to tackle the factorization
problem. Experimental demonstrations are conducted for the factorization of
small composite numbers such as $6 = 2 \times 3$, $15 = 3 \times 5$, and $35 =
5 \times 7$. This approach involves employing Rydberg-atom graphs to
algorithmically program binary multiplication tables, yielding many-body ground
states that represent superpositions of factoring solutions. Subsequently,
these states are probed using quantum adiabatic computing. Limitations of this
method are discussed, specifically addressing the scalability of current
Rydberg quantum computing for the intricate computational problem.
