The Chinese dragons have five toes on each foot, Indonesian or Korean dragons have four, and the Japanese dragons have three. To explain this phenomenon, Chinese legend states that all Imperial dragons originated in China, and the further away from China a dragon went the fewer toes it had. Dragons only exist in China, Korea, Indonesia, and Japan because if they traveled further they would have no toes to continue. The Japanese legend has a story similar to the Chinese one, namely that dragons originated in Japan, and the further they traveled the more toes they grew and as a result, if they went too far they would have too many toes to continue to walk properly.
Official interpretation back in the dynasty period: Five claws dragons are reserved for the emperors (five is the holy number in Five elements (Chinese philosophy), four claws dragon is reserved for kings, princes and certain high rank officials, three claws dragon are used by the general public(which is widely seen on China and other Chinese goods back in Ming dynasty). Since Korea and other nations only held the title of king (with respect to the emperor in china), they are only allowed to use four claw dragon. Inproper use of claw number is considered as a sign of rebellion, and will be punished heavily such as executions of whole clan.
Another interpretation: according to several sources, including historical official documents, ordinary Chinese dragons had four toes - but the Imperial Dragon had five. It was a capital offense for anyone - other than the emperor, his blood relatives, and the very few officials who were granted such an extraordinary privilege by the emperor - to use the five-clawed dragon motif.
Korean sources seem to oppose this theory, as the Imperial dragon in Gyeongbok Palace has seven claws, implying its superiority over the inferior Chinese Dragon; of course, this dragon image is hidden in the rafters of the palace and is not entirely in view, even to those who know it is there, suggesting that while the ancient Koreans viewed it as superior, they also knew that it would be offensive to the Imperial Chinese Court.
The Han style dragon is also 3 clawed, which explains how the 3 clawed dragon went to Japan in the Tang or pre-Tang period.