Bob told you right, the 36th. FA Bn was never a division member. It may have fired in support of the 3rd. ID, as well as various other componants, but it did not belong to the 3rd. or to any other division.
A brief history, in addition to what Bob posted:
It started out as the 36th. FA Regiment (155mm gun, motorized); activated 10 Oct 39, Fort Bragg, NC, and attached to I Army Corps;(read as Roman Numeral I); departed NY P/E 10 Aug 42; arvd. Scotland 17 Aug 42; dptd. England 25 Nov 42; arvd. North Africa 8 Dec 42; landed Sicily 8 Aug 43; landed Italy 21Sep 43; assaulted Anzio 22 Jan 44; redesignated in Pantano, Italy as HHB, 36th. FA Group 5 Mar 44; 1st and 2nd. BNs redesignated 36th. FA Bn and 633rd. FA BNs respectfully. CAMPAIGNS: Tunisia, Sicily, Naples-Foggia, Rome-Arno, Anzio.
A brief history of 36th. FA BN:
activated 5 Mar 44 at Nettuno, Italy (1st. BN,36th. FA BN); Italy, 5 Mar 44: France-ETO 15 Aug 44; arvd. NY P/E 7 Jan 46; deactivated Camp Kilmer, NY 8 Jan 46. Unit was at Holzhause, Germany, the day the war ended.
CAMPAIGNS: Anzio, Ardennes-Alsace (Bulge),Central Europe, Naples-Foggia,Rhineland,Rome-Arno and Southern France.
Me ? I was a Chief-of-Section, 985th. FA BN, II Corps, Fifth Army, Italy, a long, long time ago.