This question is a trap. If you try to answer it, you’ll find yourself beset by semantic questions. What’s intelligence? What’s a factor? And if you get past those, you’ll then find a bleak valley of statistical arcana. What do the eigenvalues look like? Do they imply causality?
This is all backward. If your goal is to understand the external world, you can skip the hand wringing and start by looking at the damn data. So let’s do that.
To start, let’s forget about intelligence, and ask an easier question: Does it make sense to refer to some people as “more physically fit” than others? Is that reasonable, or do we need to break things down by strength, speed, coordination, etc.?
To answer this, I looked for studies that gave people batteries of different physical tests. I found three that make enough information available to analyze.
Here are the correlations among the different tests (click to open/close). The columns are the same as the rows—so the 3rd square in the first row is the correlation between hand grip and pull-ups.