WRONG RWY LNDG ON A CLOSED RWY BY A LOW TIME PA28-180 PVT PLT WITH A CFI FRIEND GOING ALONG FOR THE RIDE TO JVL; WI.

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THIS WAS A PLEASURE FLT; ALTHOUGH I AM A CFI; I WAS ALONG FOR THE RIDE. THE TWR AT THE CLASS D ARPT HAD CLRED THE PIC TO LAND ON RWY 36; #2. WE WERE COMING FROM THE SW; AND WE WERE LOOKING FOR THE OTHER TFC. UNABLE TO SEE THEM; I ASKED THE TWR WHERE THE TFC WAS; AND THEY SAID IT WAS ON SHORT FINAL; NO FACTOR. IT LOOKED LIKE WE WERE LINED UP WITH RWY 36. NORMALLY; I WOULD HAVE THE STUDENT LOOK AT THE HDG ON THE DG TO CONFIRM WE WERE ON THE RIGHT RWY; BUT I WAS JUST ENJOYING THE FLT. AFTER LNDG; THE TWR ASKED THE PIC IF SHE WAS A STUDENT PLT. SHE ANSWERED 'NO.' THEN TWR INFORMED HER SHE HAD LANDED ON RWY 4; WHICH WAS CLOSED. I NEVER SAW THE RWY NUMBER WHEN WE WERE LNDG; OR ANY INDICATION THE RWY WAS CLOSED. I FAILED TO LOOK AT THE DIRECTIONAL GYROSCOPE ON FINAL TO CONFIRM THE CORRECT RWY; BUT I WAS NOT ACTING AS INSTRUCTOR. I AM FILING THIS RPT IN CASE THE FAA HOLDS ME RESPONSIBLE. I KNOW WE WERE AT FAULT; BUT I AM SURE TWR SAW WHAT WAS HAPPENING AND DECLINED TO SHARE IT WITH US. THE WAY TO KEEP THIS FROM HAPPENING AGAIN; IS NOT LET YOURSELF GET DISTR LOOKING FOR TFC AND FORGET THE IMPORTANT THINGS; LIKE LNDG ON THE CORRECT RWY.