We need $462 / n$ to be an integer, so $n$ must be a divisor of 462 .
Checking the options:
- $\(4 \rightarrow 462 \div 4=115.5\)$, not integer.
- $\(5 \rightarrow 462 \div 5=92.4\)$, not integer.
- $\(9 \rightarrow 462 \div 9=51.33 \ldots\)$, not integer.
- $\(13 \rightarrow 462 \div 13=35.538 \ldots\)$, not integer.
- $\(22 \rightarrow 462 \div 22=21\)$, integer.

Thus, the value of $n$ that works is 22 .