  We give an overview of combinatoric properties of the number of ordered
$k$-factorizations $f_k(n,l)$ of an integer, where every factor is greater or
equal to $l$. We show that for a large number $k$ of factors, the value of the
cumulative sum $F_k(x,l)=\sum\nolimits_{n\leq x} f_k(n,l)$ is a polynomial in
$\lfloor \log_l x \rfloor$ and give explicit expressions for the degree and the
coefficients of this polynomial. An average order of the number of ordered
factorizations for a fixed number $k$ of factors greater or equal to 2 is
derived from known results of the divisor problem.
