[tex]U\Big(2^{30}+3^{31}+5^{32}+6^{33}\Big) = \\ \\ = U\Big(4^{15}+3^{30}\cdot 3+5+6\Big) = \\ \\ = U\Big(64^5+27^{10}\cdot 3+11\Big) = \\ \\ = U\Big(4^5+7^{10}\cdot 3+1\Big) = \\ \\ = U\Big(64\cdot 4^2+49^5\cdot 3+1\Big) = \\ \\ = U\Big(4\cdot 16+9^5\cdot 3+1\Big) = \\ \\ = U\Big(4+9^4\cdot 9\cdot 3+1\Big) = \\ \\ = U(5+1\cdot 9\cdot 3) = U(5+7) = \boxed{2}[/tex]
