The HCF of two numbers is $4$ and their LCM is $5940$. If one of the numbers is $108$, what is the other number?

We know the fundamental relationship between two numbers and their HCF and LCM:
$$\text{First Number}\times \text{Second Number}=\text{HCF}\times \text{LCM}$$

Given:

* $\text{HCF}=4$
* $\text{LCM}=5940$
* $\text{First Number}=108$

Let the second number be $x$. Substituting these values into the formula:

$$108\times x=4\times 5940$$

$$x=\frac{4\times 5940}{108}$$

Simplify the expression:

$$x=\frac{5940}{27}$$

$$x=220$$

Therefore, the other number is $220$.