"F) Finally, we may define $\displaystyle Pic(X)$ to be the group $\displaystyle Div(X)/$(pinc. divisors). Then $\displaystyle R_X$ itself is a UFD if and only if $\displaystyle Pic(X)=(0)$."

This part is the 6th line from the top on the page 19 of "Algebraic geometry 1:Complex Projective Varieties(by David Mumford)"

Can you prove this?

Please, explain to me...