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
.