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According to The Pacific War: Japan Versus the Allies by Alan J. Levine, corruption was a partial cause:
... The Chinese Army nominally had no less than 182 infantry divisions against 21 regular Japanese divisions. But most Chinese units were actually at half-strength or less, thanks partly to the amiable custom of having commanders pay their own troopsβthe fewer men a commander had, the more money he could pocket for himself. ...
Wikipedia also suggests that it was due to bickering warlords who could not agree on whose divisions would be merged or disbanded, also citing corruption as a cause:
In 1934 Gen. Hans von Seeckt, acting as advisor to Chiang, proposed an "80 Division Plan" for reforming the entire Chinese army into 80 divisions of highly trained, well-equipped troops organised along German lines. The plan was never fully realised, as the eternally bickering warlords could not agree upon which divisions were to be merged and disbanded. Furthermore, since embezzlement and fraud were commonplace, especially in understrength divisions (the state of most of the divisions), reforming the military structure would threaten divisional commanders' "take".
Eventually the NRA simply compensated by using corps, composed of 2-3 divisions, as the basic tactical unit:
The Chinese Republic had 133 Corps during the Second Sino-Japanese War. After losses in the early part of the war, under the 1938 reforms, the remaining scarce artillery and the other support formations were withdrawn from the Division and was held at Corps, or Army level or higher. The Corps became the basic tactical unit of the NRA having strength nearly equivalent to an allied Division.
So in order to compare formations, you can divide the number of Chinese divisions by 2 or 3 to get the actual strength in numbers.