It sounds like you're counting activities.
Counts are not factors. They're numeric variables with a meaningful 0 and equal intervals.
Just because they're discrete rather than continuous doesn't make them factors, and you should not in normal circumstances seek to turn them into factors.
Making a count variable a factor throws away a lot of information.
There may be situations where you might seek to treat that "number of activities" as some ordered factor rather than interval, but generally you'd avoid treating it as nominal categories.
(In your particular case, if the effect of adding each new activity to the count is thought to be arbitrary -- so that intervals aren't expected to be equal or even smoothly changing -- then you might treat it as ordered categories, but you'd seek to avoid just making it a factor and throw away the ordering.)
Response to question in comments:
Well I don't want to attach undue importance to the Stevens typology, but since you frame the question that way, I'll mostly use it for the moment. Please note that it's not the only way to think about analysis (there are other typologies, for example), and it's not always helpful -- if it leads you to throw away useful or important information, it's not helping you.
The thing is "being integers" doesn't make it ordinal. Normally, anything with equal intervals is best treated as numerical (at least interval), but it depends on how you're using it in the model (the typology shouldn't drive the analysis; the needs of the analysis should).
Kelvin - to some extent it depends on the model, but discretized temperatures in Kelvin would normally be considered ratio scale (or at least interval scale if the fact that it has a meaningful zero didn't matter for the model); in other typologies they still would be numeric variables.
Age - again, it depends on your model, but age will usually tend to be at least interval (another year is another year, whether you're 15 or 64), and in some cases ratio (for example, if you're looking at lifetime exposure to background radiation, that zero means something). In some cases you might regard it as ordinal.
How about dates? I'm guessing they must be counted as factors.
Must? Well, no. In many cases, you convert them to a time interval from some origin, which makes the converted values (typically) interval, since (again), a year is a year and a day is a day. (Again, however, it depends on the model. In some cases, there's also a particular event date and later dates represent some kind of exposure time or survival time from that event - ratio. In other cases they might be treated as ordered categories.)
Can we take nominal and ordinal variables in general to be factors?
Usually you'd do that, yes. Certainly with nominal variables. With ordered categories generally speaking the ordering contains a lot of information that should be retained, and so it's common to treat the factors differently. Sometimes ordered categories are treated as interval (when people add Likert-scale questionnaire items, for example, to make an actual Likert-scale, but also in other circumstances). R certainly treats ordered factors quite differently.
or any more exceptions that I should be watchful of?
Rather than try to find lists of exceptions (which sounds like a lot of work, and would be unlikely to be complete), it's a matter of considering what the available information is, and how you'll be using it in your model.