[Adm.Lee]

As an expansion of the above....

Infantry regiments were originally assigned during WWI, when the National Guard received those 26-50 numbers. Each division had 2 brigades, each of 2 regiments, and these were numbered to match. So, my home state of Ohio's 13 infantry regiments and 1 battalion (colored) were shuffled about to become the 37th Division, with the 73rd and 74th Brigades, 145th-148th Infantry Regiments. Also, the 112th MP Company, 112th Medical Detachment, 112th this, 112th that, and so on. The Field Artillery Brigade was the 62nd, and its three regiments were the 134th-136th. These got scrambled a bit during the early stages of WW2 (I have a big list of Ohio's NG units) and more so since then.

Note that if you multiply the division number by 2, you can derive the infantry brigade numbers, and if you multiply it by 4, you can tell the regiment's numbers. This worked for British brigades (certainly not battalions) in both World Wars, too-- 3 brigades per division-- the 51st has the 151, 152, 153 brigades, and so on.

This worked for the NG and AUS (draftee) divisions, but not the Regulars, since those were assembled by putting together what regiments they could find. I'm pretty sure I read that the 1st Division formed around New York City, and the 16th, 18th, 26th and 28th regiments were based or organized from there.

When the regiments were broken up after Korea, they started assigning regimental numbers to battalions that had some affiliation with their parent division. This eventually went giggle-piggledy, and you've got what you see today (if you can bear to look at it).

When Gens. Marshall and McNair started raising the many new units and formations they would need for WW2, they used numbers to help ID some combat units types.
100s- lots of field artillery brigades, but I'm not sure if that's on purpose.
500s- parachute infantry regiments or battalions, but the glider regiments kept the numbers of their parent divisions. Thus the 325th (close to 4x82) stayed in the 82nd Airborne Division.
600s- some antitank/tank destroyer battalions
700s- tank battalions not in armored divisions, some tank destroyer battalions (converted from tank units?)
800s- tank destroyer battalions
900s- engineer construction regiments
1000s- engineer special or port brigades
1100s- engineer combat brigades
Field artillery had its own numbering, I haven't picked up the pattern, if any. Often, they kept the numbers of the regiments they replaced.

Artillery & engineer battalions, service units, support units: I got nuthin'