The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. By far, there is no experimental realization of adiabatic quantum computation on a single solid spin system under ambient conditions, which has been proved to be a compatible candidate for scalable quantum computation. In this letter, we report on the first experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution, and final state readout, are realized experimentally. As an example, we factored 35 into its prime factors 5 and 7 on our adiabatic quantum processor.The nitrogen-vacancy (NV) center in diamond is an excellent quantum processor and quantum sensor at room temperature [1].The spin qubits of NV center are promising for quantum information processing due to fast resonant spin manipulation [2], long coherence time [3,4], easy initialization and read-out by laser illumination [5]. Many quantum gates [6-9], quantum algorithms [10], quantum error corrections [11,12] and quantum simulations [13,14] have been demonstrated on it. However, so far no adiabatic quantum algorithm has been realized on this system. In circuit-model quantum computation, the computational process is implemented by a sequence of quantum gates. In 2000, Farhi et al.[15] developed another architecture of quantum computation, i.e., the adiabatic quantum computing (AQC), in which the computational process can be realized through the adiabatic evolution of a system's Hamiltonian, and it is proved to be equivalent to circuit model quantum computing [16].In contrast to multiplying of large prime numbers, up to now, no efficient classical algorithm for the factorization of large number is known [17]. Previously, many experimental work on large number factorization have been done based on Shor's algorithm [18][19][20][21][22][23][24]. To demonstrate the AQC on the room temperature single spin system, we take 35 as an example and factored it on the adiabatic quantum processor. The core idea used here is to transform a factorization problem to an optimization problem and solve it under the AQC framework [25,26].Generally, to solve a problem under the AQC framework, first we need to find a problem Hamiltonian H p , and the solution of the problem is encoded in the ground state of H p . We start from the ground state of H 0 and the Hamiltonian of the evolution progress is H(t) =(1 â s(t))H 0 + s(t)H p , s(0) = 0, s(T ) = 1.(1)Where T is the total evolution time, and the whole system is governed by the Schrödinger equation