Earlier quoted context omitted.
Go ahead and tell that to everyone who has been using that phrase to mean what I describe. I seriously searched for a single case of someone using the phrase in the manner you're insisting is correct and came up empty. Instead, I found a large number of resources backing up what I and OP have been stating. Even many professional mathematicians acknowledge the ambiguity but agree that the phrase means to multiply. You…
Thanks for posting the first few links from using Google. Here are some other links from Google that explains why your vociferous insistence is wrong. http://www.crackssat.com/isee/word-problems/question-250-ans... https://english.stackexchange.com/questions/8680/how-much-ex... https://forum.wordreference.com/threads/increase-by-a-factor... https://books.google.com/books?id=wDKLXdzQL5AC&pg=PA182&lpg=... http://econlo…
You seem to be stuck on the translation here. These are two different phrases with different meanings. Yes, they both refer to increases. Yes, they both can be interpreted as multiplications on the original term. No, they are not the same. You found exactly one case which does not use the same verbage and specifically points to percentages. I don't know how else to say that different phrases in English carry different meanings. You can't just say "a factor of X" is equivalent to "X00%". This just is not understood to be true. Even the GMAT and GRE present questions in this way with the understanding that "a factor of X" means to multiply by X.
I'm not going to continue to explain this to you. There's really nothing more to be said. If you attempt to solve problems presented in the format of "increased by a factor of X" such that X is not presented as a percentage, you will be marked as incorrect more often than not.
I'm not even explicitly arguing for a populism argument. I'm stating that the problem is presented in a different format than you are claiming it to be.