  In the article integer divisibility properties and related prime factors
natural number representation concepts have been defined over the whole
infinite hyperoperation hierarchy. The definitions have been made across and
above of unique arithmetic operations, composing this hierarchy (addition,
multiplication, exponentiation, tetration and so on). It allows the habitual
concepts of "prime factor", "multiplier", "divider", "natural number factors
representation" etc., to be associated mainly with the same sense, with the
each of those operations. As analogy of multiplication-based Fundamental
Theorem of Arithmetic (FTA), an exponentiation-based theorem is formulated. The
theorem states that any natural number $M$ can be uniquely represented as a
tower-like exponentiation: $M=a_n\uparrow(a_{n-1}\uparrow (\ldots (a_2\uparrow
a_1)\ldots )),$ where $a_i\neq 1 (i=1,\ldots,n)$ are primitive in some sense
(related to the exponentiation operation), exponentiation components, following
one by one in some unique order and named in the article as biprimes.
