  The problem to express a natural number N as a product of natural numbers
without regard to order corresponds to a thermally isolated non-interacting
Bose gas in a one-dimensional potential with logarithmic energy eigenvalues.
This correspondence is used for characterising the probability distribution
which governs the number of factors in a randomly selected factorisation of an
asymptotically large N. Asymptotic upper bounds on both the skewness and the
excess of this distribution, and on the total number of factorisations, are
conjectured. The asymptotic formulas are checked against exact numerical data
obtained with the help of recursion relations. It is also demonstrated that for
large numbers which are the product of different primes the probability
distribution approaches a Gaussian, while identical prime factors give rise to
non-Gaussian statistics.
