jmc

From the given information, the positive factors of $x$ include $1,3,\frac{x}{3}$, and $x$. Therefore, we must have $1+3+\frac{x}{3}+x\le 24$. Simplifying, we find $x\le 15$. Testing $x=15$, we succeed: $1+3+5+15=24$. We try 3, 6, 9, and 12 to confirm that only 15 yields a sum of 24. Thus, $x=\boxed{15}$.