'Favourite' and 'favorite' both mean the same. While the former (favourite) is used in British English, the latter (favorite) is American English.
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There are a number of these:
color / colour, rancor / rancour, humor / humour.
The main purpose of their existence seems to be to confuse learners and incite friendly argument among native speakers.
A simplified summary from Wikipedia:
Many of the now characteristic American English spellings were introduced, although often not created, by Noah Webster in his An American Dictionary of the English Language of 1828.
Webster was a strong proponent of spelling reform for reasons both philological and nationalistic. Many spelling changes proposed in the U.S. by Webster hi
00Well, in my class of English literature, a couple of year ago, I saw a documentary made by CBC and ABC showing how spelling of a lot of words changed within the community of the settlers of the Thirteen Colonies in 18th century (1700 to 1800 for those "01i00uneducated02i00" americans 05000 lol i'm gonna be shot for this... lol).02p
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