I’ve noticed that the army skipped over many division numbers during WWII. For the infantry divisions this was: - 12 - 14-16 - 18-22 (and 23 if the Americal Division is taken into account) - 39 - 64 - 67-68 - 72-74 - 105

(The above does not include the 10th Mountain Division, and the 11th, 13th, 17th, 82nd and 101st Airborne Divisions, which I counted as infantry divisions).

For the armored divisions this was: - 15-19

The numbering system of U.S. Army divisions that was used during World War II and continues in some form to the present day has its genesis in the summer of 1917 during World War I:

The War College Division and the adjutant general created yet another system for designating divisions and brigades and their assigned elements. Divisions were to be numbered 1 through 25 in the Regular Army, 26 through 75 in the National Guard, and 76 and above in the National Army. Within the Regular Army numbers, mounted or dismounted cavalry divisions were to begin with the number 15. The National Defense Act of 1916 provided for sixty-five Regular Army infantry regiments, including a regiment from Puerto Rico. From those units, excluding the ones overseas, the War Department could organize thirteen infantry divisions in addition to the 1st Expeditionary Division already in France. This arrangement explains the decision to begin numbering Regular Army cavalry divisions with the digit 15. The system did not specify the procedure for numbering National Guard or National Army cavalry divisions. It reserved blocks of numbers for infantry, cavalry, and field artillery brigades, with 1 through 50 allotted to the Regular Army, 51 through 150 to the National Guard, and 151 and above to the National Army.

When the National Guard was reorganized after World War I, units were authorized by the National Defense Act amendments of 4 June 1920 to keep their "names, numbers and other designations, flags, and records...as far as practicable." However, this did not mean that units would necessarily always be assigned to the same higher organizations as they had been during the World War. Because of modifications required with the new troop basis, some units disappeared entirely; this situation would sometimes be corrected because of pressure from state adjutants general, who were eager to preserve the lineages of their units.

The National Guard was allotted the 26th through 45th Divisions, less two (the 31st Division, and the 42nd Division, which had made up of units from twenty-six states and the District of Columbia during the World War). The 43rd-45th Divisions were new units, so some shuffling of states was necessary. The divisions of the wartime "National Army" (the conscript army) were allotted to the new Organized Reserve, and in most cases, continued the rough geographic allocations of their predecessors. These began with the 76th Division, through the 104th, less two; the 92nd and 93rd Divisions, formed as segregated (African American) divisions during the war, were initially not reformed.

In 1920, the designations of three divisions (the 30th, 31st, and 39th) were offered to the staff of the Fourth Corps Area (initially comprising the states of Arkansas, Florida, Georgia, Louisiana, Mississippi, North Carolina, South Carolina and Tennessee), who could pick two. The designations of the 30th (Georgia, North Carolina, South Carolina, and Tennessee) and 39th (Alabama, Arkansas, Florida, Louisiana, and Mississippi) were initially chosen. On 1 December 1920, responsibility for Arkansas was shifted from the Fourth Corps Area to the Seventh Corps Area (comprising also Iowa, Kansas, Minnesota, Nebraska, Missouri, North Dakota, and South Dakota). In 1923, the adjutants general of the states concerned in the Fourth Corps Area petitioned the War Department to change the designation of the 39th Division to the 31st, as during World War I, the 31st Division had been made up of troops from Alabama, Florida, and Georgia, and the 39th from Arkansas, Louisiana, and Mississippi, and the former division was the division in which most of the affected units had served. This request was granted, and the designation of the 39th Division was changed to the 31st on 1 July 1923. The 39th Infantry Division did not come into existence again until 1946, as a National Guard division from Arkansas and Louisiana. It served until 1967.

Concerning the other divisions, many of these units had been constituted (placed on the rolls of the Army) during World War II, but were dropped from the mobilization program and never activated as the number of divisions the Army felt necessary to win the war became clearer in 1943. The troop basis issued in 1943 called for 100 divisions (sixty-two infantry, twenty armored, ten motorized, six airborne, and two cavalry divisions); twelve of these divisions were later deferred and then dropped from the troop basis entirely, giving a grand total of eighty-eight. Two light divisions (the 71st and 89th) were later given permanent status, making ninety (sixty-seven infantry, two cavalry, sixteen armored, and five airborne divisions). One division (the Philippine Division) was surrendered in 1942, while another (the 2nd Cavalry Division) was activated and inactivated twice.

The 15th, 17th, and 18th Armored Divisions were constituted, but never activated, as were the 61st, 62nd, 67th, 68th, 72nd-74th, 105th, and 107th Infantry Divisions. Like the armored divisions, the infantry divisions were constituted in the Army of the United States. The 105th and 107th Infantry Divisions were supposed to be additional segregated infantry divisions. It was intended that the 92nd Infantry Division was to furnish the cadre for the 105th, and the 105th for the 107th, but a shortage of personnel because of more pressing needs prevented them from ever being formed.

The Panama Canal, Hawaiian, and Philippine Divisions contained the units intended to form the "10th," "11th," and "12th" Divisions, but they received names, rather than numbers because they were intended for wartime employment in specific geographic areas. The Panama Canal Division headquarters was inactivated in 1932 and its forces were assigned to the "Atlantic" and "Pacific" Sectors. The division was disbanded in 1938. A division-like structure, the Panama Mobile Force, was in existence in 1940 and 1941. The Philippine Division was briefly activated as the 12th Infantry Division postwar, but was inactivated in 1947.

Table: Intended Composition of Divisions Constituted But Never Activated

Division	Infantry	Field Artillery
15th Airborne Division	191st, 192nd, 545th Infantry Regiments	459th Parachute, 678th and 679th Glider Field Artillery Battalions
61st Infantry Division	247th-249th Infantry Regiments	716th, 855th-857th Field Artillery Battalions
62nd Infantry Division	250th-252nd Infantry Regiments	717th, 858th-860th Field Artillery Battalions
67th Infantry Division	265th-267th Infantry Regiments	722nd, 873rd-875th Field Artillery Battalions
68th Infantry Division	268th-270th Infantry Regiments	723rd, 876th-878th Field Artillery Battalions
72nd Infantry Division	280th-282nd Infantry Regiments	721st, 858th-860th Field Artillery Battalions
73rd Infantry Division	283rd-285th Infantry Regiments	722nd, 873rd-875th Field Artillery Battalions
74th Infantry Division	286th-288th Infantry Regiments	723rd, 876th-878th Field Artillery Battalions
105th Infantry Division	419th-421st Infantry Regiments	585th-588th Field Artillery Battalions
107th Infantry Division	308th, 312th, 316th Infantry Regiments	Undesignated field artillery composition

The 308th, 312th, 316th, and 419th-421st Infantry Regiments had existed previously. The 308th (77th Division), 312th (78th Division), 316th (79th Division), and 419th (94th Division) Infantry Regiments were Organized Reserve units and had been inactivated by relief of personnel when their parent divisions were ordered into active military service in 1942 and reorganized from "square" to "triangular" divisions.

The 420th and 421st Infantry Regiments were Organized Reserve light tank units (during the interwar period and before the creation of the Armored Force, tanks were under the legal control of the Infantry branch), but were never ordered into active military service under these designations. On 30 January 1942, the 421st Infantry Regiment was reorganized and redesignated as the 782nd Tank Battalion (Light). This battalion was activated at Camp Campbell, Kentucky, on 1 February 1943 and inactivated at Fort Bragg, North Carolina, on 25 February 1946. The 421st Infantry Regiment was reconstituted in the Army of the United States on 5 May 1942 as part of the 105th Infantry Division, but was never activated and was disbanded on 4 August 1952.

Many divisions, especially those with very high numbers, were purely nonsensical and used to confuse the German high command during deception operations preceding the D-Day landings, such as the 6th, 9th, 18th, 21st, and 135th Airborne Divisions, and the 11th, 14th, 17th, 18th, 22nd, 46th, 48th, 50th, 55th, 59th, 108th, 119th, 130th, 141st, and 157th Infantry Divisions.

1/2

The skipped numbers are not entirely explicable, but we can explain some of them. In WWII, the U.S. Army wasn't just raising divisions but in many cases activating existing units.

Infantry Divisions

Basically, there was an orderly system before WWI that was replaced by another orderly system for WWI that was mostly retained between the wars, before it got a bit messed up by WWII.

Pre-WWI

In the pre-WWI Army, there were notionally 20 divisions of infantry (the term "Infantry Division" didn't come along until just before the United States entered WWII) and they were numbered sequentially:

Regular Army: 1st-4th

National Guard (state militia): 5th-20th, which were allocated in a geographical sequence starting in the New England and ending in the Pacific Northwest.

In 1916 as American involvement in WWI loomed, Congress authorized a huge in the Army's budget, including a big increase to the sizes of all components. The Army liked order and so reallocated the numbers:

Regular Army: 1st-25th

National Guard: 26th-75th, which necessitated adding 21 to the existing divisions' numbers.

National Army (draftees in completely new formations): 76th+

WWI

So during mobilization for WWI, the numbers were actually used in order within those bands. This resulted in the following numbers actually being used:

Regular Army: 1st-20th

National Guard: 26th-42d, with 26th-41st being prewar units and the 42d being the famous "Rainbow Division" composed of small National Guard units that hadn't been assigned to the other divisions

National Army: 76th-102d, not all of which were fully constituted for deployment and combat, of which the 92d and 93d were "colored" i.e. African-American formations and the 94th was recruited from Puerto Rico. (The 94th lost its association with Puerto Rico immediately after WWI.)

Interwar

After WWI, the Army demobilized. The Regular Army downsized such that only parts of the 1st through 9th Divisions remained. The 10th through 20th were disestablished and their numbers were freed up. The Regular Army also referred to its division-sized garrisons in Hawaii, the Panama Canal Zone, and the Philippines as named (not numbered) divisions.

The National Guard, on the other hand, expanded slightly and used the numbers 26th through 45th, with the exception of the 39th and 42d. The 39th Division is missing because, as various National Guard units were shuffled around between divisions, the 39th Division was felt to be a better match with geographical territory associated with the wartime 31st Division, so it was assigned that number and there was no 39th Division. The 42d Division, as noted, had been a wartime expedient and didn't belong to a particular region, but its number was famous and couldn't just be reassigned (at least not yet).

With two exceptions, the National Army divisions were retained as components of the Organized Reserve with a small cadre of reserve officers assigned in peacetime and the expectation that the units would be filled out come war. These divisions also had regional associations. Two more such divisions were added shortly after WWII so the full list was 76th through 104th. But, as you may have predicted, the 92d and 93d Divisions (with black soldiers) were not retained in any form.

WWII

So for WWII mobilization we basically see a lot of order but also some chaos. Also, the divisions we are discussing started to be called "Infantry Divisions." It's also important to keep in mind that the Army stopped forming new divisions at the end of 1943, making the so-called 90-division gamble. Even though the United States could have fielded hundreds of army divisions and had really expected to do, the decision was made to limit the number to 90: 67 infantry, 2 cavalry, 16 armored, 5 airborne. (You did not ask about the cavalry divisions, probably because it's super-boring: 1st and 2d Cavalry Divisions, no mystery.)

First, order. The Regular Army filled out the 1st through 9th Infantry Divisions. The National Guard was mobilized, which accounts for the 26th through 38th, 40th, 41st, and 43d through 45th Infantry Divisions. (We have already seen why the 39th and 42d were missing.)

The high-numbered divisions from the old National Army which had made it through the war as Organized Reserve units were also filled out which gets us the 76th through 91st and 94th through 104th Infantry Divisions. This was not actually done in numerical order: the War Department made a list based on the divisions' WWI combat records and activated them in that order.