I4.3 Let $f$ be a function satisfying the following conditions:
(i) $f(n)$ is an integer for every positive integer $n$;
(ii) $f(2)=2$;
(iii) $f(m n)=f(m) f(n)$ for all positive integers $m$ and $n$ and
(iv) $f(m)>f(n)$ if $m>n$.
If $C=f(B)$, find the value of $C$.
$\begin{array}{l}2=f(2)>f(1)>0 \Rightarrow f(1)=1 \\ f(4)=f(2 \times 2)=f(2) f(2)=4 \\ 4=f(4)>f(3)>f(2)=2 \\ \Rightarrow f(3)=3 \\ C=f(12)=f(4 \times 3)=f(4) f(3)=4 \times 3=12\end{array}$