Matched witness for multipartite entanglement

Entanglement criteria for multipartite entangled states are obtained by matching witnesses to multipartite entangled states. The necessary and sufficient criterion of separability for three qubit X states is given as an example to illustrate the procedure of finding a criterion. The result is utilized to obtain the noise tolerance of W state. The necessary and sufficient criteria of three partite separability and full separability for four qubit noisy cluster states, three partite separability for four qubit noisy GHZ states are obtained.