Find the greatest number that exactly divides $187$ and $391$.

The greatest number that exactly divides both numbers is their Highest Common Factor (HCF).
Let's find the prime factorization:

$$187=11\times 17$$

$$391=17\times 23$$

The common prime factor is $17$. Hence, the $\text{HCF}$ of $187$ and $391$ is $17$.