Answer is: 65

\(\rightarrow \ \text{ Molecular formula of Thyroxine }\ \Rightarrow\) \(\mathrm{C}_{15} \mathrm{H}_{11} \mathrm{O}_{4} \mathrm{NI}_{4}\)
\(\rightarrow \text{ Molecular mass of Thyroxine -}\)
\(
C \rightarrow 15 \times 12=180\)
\(
\mathrm{H} \rightarrow 11 \times 1=11\)
\(
\mathrm{O} \rightarrow 16 \times 4=64\)
\(
\mathrm{N} \rightarrow 14 \times 1=14\)
\(
I \rightarrow 127 \times 4=508\)
\(\rightarrow \text{Molecular mass of Thyroxine }\Rightarrow 777\)
\(
\rightarrow \%\ \text{of Iodine }=\frac{508}{777} \times 100\)
\(=65.38 \%\)
\(
\text{Nearest integer} =65\)