"a common fact" is a correct and usable phrase in written English. You can use it to refer to a statement that is widely accepted or known to be true. For example, "We all know that the Earth revolves around the Sun is a common fact.".
"It's just a common fact of life for men".
Another theory refers to a common fact of the members' résumés: Junior Achiever, Somewhat Older Now.
THE car bomb, whether guided by a suicidal driver or not, is a common fact of modern life.
Furthermore, quality variations in cadmium platings used in aircraft components are a common fact.
It is a very common fact that people respect you only when you respect yourself.
It is a very common fact that women feel that make-up makes them sexy and alluring to the opposite sex.
Bomb blasts are an ugly but common fact of life -- not quite routine, but far from exotic or unusual -- in South Asia, and they have been since long before 9/11.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.