The context is "Every 3 year the total area is increased by a factor of order 3 by adding more stations". I understand that "increase by a factor 10" means increase to 10 times of the original thing, but what is "a factor of order 3"? Thank you very much for your help.
Without seeing the phrase in context, I can't say for sure, but my best guess is that the author is using "of order 3" to mean "approximately 3". Or more precisely, I suspect they mean either
- "closer to 3 than to 1 or 9" (because 9 = 32)
- "closer to 3 than to 0.3 or 30" (which are 3/10 and 3×10 respectively)
It's impossible to tell based on the information given which of these (if either) was meant, but use of the word "order" implies that the difference between the two of them is not too important anyway.
The phrase "of order [number]", if [number] is a power of 10, is often used to mean "closer to [number] than to any other power of 10". Sometimes people generalize this to use similar phrasing with other numbers like 2, 3, or 5 in which case "of order [number]" can mean "closer to [number] than to any other power of [number]", or it can mean "closer to [number] than to [number/10] or [number ×10]".