  D. Hensley showed in 1994 that the number of steps taken by the Euclidean
algorithm to find the greatest common divisor of two natural numbers less than
or equal to n follows a normal distribution in the limit as n tends to
infinity. V. Baladi and B. Vall\'ee subsequently gave an alternative proof for
both the classical Euclidean algorithm and several of its close variants, based
on a detailed investigation of spectral properties of the transfer operator
associated to the Gauss map, building on deep results of D. Dolgopyat. In this
article we give a much shorter, albeit less quantitative, proof of this result
using only basic spectral properties of the transfer operator together with the
method of moments and a Tauberian theorem due to H. Delange.
