"A is bigger than B by a factor of two" means that A is two times as large as B. "A is bigger than B by a factor of ten" means that A is ten times as big as B. It is language associated with science and engineering. One reason for using it is that the financial language of percentage increases starts to be confusing if the difference is more than a two-digit percentage. For example, if A is an investment of $10,000 we all know "A grew by 10%" means it became $11,000. However, consider the case where A grows to $100,000. It is a little hard to know how to say it. "It grew 900%" is correct, but mentally troubling. We really want to say something with "ten" in it, and have our listener know immediately, without thinking, that we are talking about the total size of B, not the difference between A and B. "It grew by a factor of 2" is fairly short and unambiguous. It also works with numbers that are not integers. We can say "It grew by a factor of 2.5" and that's just as clear. For "2" we can say "it doubled," but there isn't any word I know of for "sesquidoubled" or "double-and-a-halfed!" A related usage is "grew by an order of magnitude," which means "a factor of ten." "Three orders of magnitudes" means "a factor of a thousand." "Orders of magnitude bigger" is an indefinite statement, it means "much, much bigger, not a few percent, not twice, not even ten times... hundreds or thousands or tens of thousands times bigger."

In this context, a factor of two means double the price.