Conventional computers operate deterministically using strings of zeros and ones called bits to represent information in binary code. Despite the evolution of conventional computers into sophisticated machines, there are many classes of problems that they cannot efficiently address, including inference, invertible logic, sampling and optimization, leading to considerable interest in alternative computing schemes. Quantum computing, which uses qubits to represent a superposition of 0 and 1, is expected to perform these tasks efficiently(1-3). However, decoherence and the current requirement for cryogenic operation(4), as well as the limited many-body interactions that can be implemented, pose considerable challenges. Probabilistic computing(1,5-7) is another unconventional computation scheme that shares similar concepts with quantum computing but is not limited by the above challenges. The key role is played by a probabilistic bit (a p-bit)-a robust, classical entity fluctuating in time between 0 and 1, which interacts with other p-bits in the same system using principles inspired by neural networks(8). Here we present a proof-of-concept experiment for probabilistic computing using spintronics technology, and demonstrate integer factorization, an illustrative example of the optimization class of problems addressed by adiabatic(9) and gated(2) quantum computing. Nanoscale magnetic tunnel junctions showing stochastic behaviour are developed by modifying market-ready magnetoresistive random-access memory technology(10,11) and are used to implement three-terminal p-bits that operate at room temperature. The p-bits are electrically connected to form a functional asynchronous network, to which a modified adiabatic quantum computing algorithm that implements three- and four-body interactions is applied. Factorization of integers up to 945 is demonstrated with this rudimentary asynchronous probabilistic computer using eight correlated p-bits, and the results show good agreement with theoretical predictions, thus providing a potentially scalable hardware approach to the difficult problems of optimization and sampling.