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It is shown how the analytic class number formula can be used to produce an algorithm which efficiently computes the class number h of an algebraic number field F. The method assumes the truth of the Generalized Riemann Hypothesis in order to estimate the residue of the Dedekind zeta function of F at s = 1 sufficiently well that h can be determined unambiguously. Given the regulator R of F and a known divisor h* of h, it is shown that this technique will produce the value of h indoi:10.1090/s0025-5718-1989-0979937-4 fatcat:wqowecyaarab3jxd64w3kgjedm