What is the difference between faster by factor and faster by percent?
Actually, if you want to use the phrase, "Faster than..." the value should be calculated as $$\frac{\text{difference between values}}{\text{value being compared to}}$$ not $$\frac{\text{value in question}}{\text{value being compared to}}$$
For example, 2 is 100% more than 1. Not 200% more.
I would say that to find the factor B is faster than A, it would be your initial calculation. 600%.
Also note that the phrases "percent faster than" or "...times smaller than" can be problematic and not as straightforward as "...times bigger". Just from an English semantics point of view. But it's generally understood what you mean.
Editing to add @pjs36 comment. When using "by a factor of", you more often see it as a number, not a percentage.
Final Edit: I would say these things.
- B is 500% faster than A
- B's speed is 600% of A's
- B's speed is 6 times as fast as A's
- B's speed is greater than A's by a factor of five(awkward IMO)
This could almost be an English question as much as mathematics. I pondered the idea (initiated by conversation about an answer I'm posting on Stack Overflow, comparing run-times for two similar coding methods), and the more I looked into it, the more confused I became - between questions on various Stack sites, Wikipedia, online "faster than" calculators, and other forums like Quora. There are many a few different answers depending on who you ask, and the context.
The basis of the calculation comes down to one rule:
Something can't be more than 100% faster than something else.
The way I figure it, the calculation for FasterThan % is:
$$\frac{({\color{Red} S}lower-{\color{Green} F}aster)}{{\color{Red} S}lower}=\%Faster Than$$
Alternatively, the calculation for SlowerThan % is:
$$\left |\frac{({\color{Green} F}aster)-{\color{Red} S}lower}{{\color{Green} F}aster} \right |=\%Slower Than$$
Example Result Pairs:
A (Slower) B (Faster)
--------------- --------------- -------------------------- -------------------------------
100 seconds 90 seconds B is 10% faster than A A is 11.1% slower than B
2 seconds 1 second B is 50% faster than A A is 100% slower than B
1.348 seconds 0.605 seconds B is 55.1% faster than A A is 122.6% slower than B
5.106 seconds 0.851 seconds B is 83.3% faster than A A is 500% slower than B
1 0 B is 100% faster than A A is infinitely slower than B
€ 100.00 € 90.00 B costs 10% less than A A costs 11.1% more than B