Find the HCF of $285,510,1440$.

Let's find the prime factorization of each given number:
* $285=3\times 5\times 19=3^1\times 5^1\times 19^1$
* $510=2\times 3\times 5\times 17=2^1\times 3^1\times 5^1\times 17^1$
* $1440=2\times 2\times 2\times 2\times 2\times 3\times 3\times 5=2^5\times 3^2\times 5^1$

To find the Highest Common Factor (HCF), we choose the lowest power of the common prime factors present in all three numbers:

* Common prime factor $3$: lowest power is $3^1$
* Common prime factor $5$: lowest power is $5^1$

$$\text{HCF}=3^1\times 5^1=15$$