A string has three resonant frequencies at 90 Hz , 150 Hz , and 210...

The resonant frequencies of a vibrating string are integer multiples of its fundamental frequency $f_0$.

Let the given resonant frequencies be $f_1 = 90 \text{ Hz}$, $f_2 = 150 \text{ Hz}$, and $f_3 = 210 \text{ Hz}$.

We have $f_1 = n_1 f_0$, $f_2 = n_2 f_0$, and $f_3 = n_3 f_0$, where $n_1, n_2, n_3$ are integers.

The highest possible fundamental frequency is the highest common factor (HCF) of the given resonant frequencies.

$f_0 = \text{HCF}(90, 150, 210)$

$90 = 30 \times 3$
$150 = 30 \times 5$
$210 = 30 \times 7$

The highest common factor is $30$.

Thus, the highest possible fundamental frequency is $30 \text{ Hz}$.