This paper introduces the Universal Divisibility Framework (UDF), a comprehensive mathematical theory that extends the classical notion of divisibility from integers to rationals, reals, and complex numbers. The framework is built upon the Universal Divisibility Function $d(a, b, c) = lfloor a/c floor (b bmod c) - lfloor b/c floor (a bmod c)$, which provides a unified criterion for divisibility across multiple number systems. We establish the Universal Divisibility Theorem, proving that for $a, b in mathbb{R}$ with $b eq 0$, and an integer $c$ satisfying $lfloor b/c floor = pm 1$, we have $b mid a$ if and only if $d(a, b, c) equiv 0 pmod{b}$. This framework not only recovers all classical integer divisibility rules as special cases but also eliminates false positives that arise when traditional rules are naively extended to non-integer domains. We provide explicit divisibility formulas for numbers 1—1000, demonstrate applications to Diophantine equations and matrix algebras, and discuss implications for computational number theory and cryptography.