Certainly it's possible; this is one of the things that LaTeX excels at. First, inside your figure, include a label by which you can refer to it:
\label{fig:coolfigure}
Then you can refer to it by figure number with \ref
or by page number with \pageref
. For example:
\documentclass{article}
\begin{document}
\section{Figures}
\begin{figure}
This is a figure
\label{fig:coolfig}
\end{figure}
Please look at Figure~\ref{fig:coolfig} on page~\pageref{fig:coolfig}.
\end{document}
This will get you the following:

Remember that the first time you run LaTeX on this, the references and their targets are being written out to the aux
file; they won't be read in correctly until you run LaTeX a second time, and it can read those references back in from the aux
file. Whenever your page numbers or references change, you'll need to run LaTeX twice to get the references to resolve correctly. Fortunately, LaTeX will tell you when this needs to happen.
\ref
is already assumed.