An N-qubit pure quantum state is “separable” if and only if it can be factored into N 1-qubit factors. Otherwise, the state is an “entangled” state. In this paper we develop two simple algorithms, one “classical” and the other “quantum”, to determine the entanglement status of an N-qubit pure quantum state. First we develop a “classical” algorithm to determine entanglement status which is of the exponential order, $O(2^N)$. We then develop an efficient “quantum” algorithm for doing the same task and it is of the polynomial order, $O(N^2)$. This new “quantum” algorithm makes use of the “quantum” speedup available for finding the “inner product” of two vectors [5]. The new “quantum” algorithm also assumes the availability of sufficiently many copies of the N-qubit pure quantum state to be tested for determining its entanglement status.