Though the word seems to have been misappropriated by bloggers and quasi-journalists as meaning “a little fact”, the word factoid actually refers to something that looks like or is presented as a fact, but isn’t.
The suffix -oid means “resembles”, it is not a diminutive suffix (that is, something you add to the end of the word to mean a smaller version, like -ette, -icle, -ling etc.).
There are many words in English that have, over the years, come to have a different meaning in popular usage than their original intended definition. For example, the word nonplussed is often used to mean “unaffected” or “calm” – its actual meaning is the exact opposite. It derivees from the Latin words non (“no”) and plus (“more”), and comes to mean a state of mind so confused or bewildered that “no more can be done about it”.
Together with ironic – which you will hear used incorrectly on a daily basis – and the made up non-word irregardless, it seems that in order to learn English, students sometimes have to learn incorrect definitions for words (or non-existent words) to understand them when they’re being used!