#### Answer

17,18

#### Work Step by Step

We take the first whole number as $x$. Since the next number will be one more than this number, the other whole number is taken as $(x+1)$.
Since the product of the consecutive whole numbers is $306$, we write the following equation and solve it:
$x(x+1)=306$
$x^{2}+x-306=0$
$x^{2}-17x+18x-306=0$
$x(x-17)+18(x-17)=0$
$(x-17)(x+18)=0$
$(x-17)=0$ or $(x+18)=0$
$x=17$ or $x=-18$
Disregarding the negative answer, we find that the smaller whole number is 17. This means that the larger whole number is 18.