Let R R be an integral domain and x ∈ R x \in R which is a product of irreducible elements. Let l ( x ) l(x) and L ( x ) L(x) denote respectively the inf and sup of the lengths of factorizations of x x into a product of irreducible elements. We show that the two limits, l ¯ ( x ) \bar l(x) and L ¯ ( x ) \bar L(x) , of l ( x n ) / n l({x^n})/n and L ( x n ) / n L({x^n})/n , respectively, as n n goes to infinity always exist. Moreover, for any 0 ≤ α ≤ 1 ≤ β ≤ ∞ 0 \leq \alpha \leq 1 \leq \beta \leq \infty , there is an integral domain R R and an irreducible x ∈ R x \in R such that l ¯ ( x ) = α \bar l(x) = \alpha and L ¯ ( x ) = β \overline L (x) = \beta .