Find the HCF of 2401,330,339

For 2401:

$$2401 = 7 \times 343 = 7 \times 7 \times 49 = 7 \times 7 \times 7 \times 7 = 7^4$$

For 330:

$$330 = 10 \times 33 = (2 \times 5) \times (3 \times 11) = 2 \times 3 \times 5 \times 11$$

For 339:

$$339 = 3 \times 113$$

(Note: 113 is a prime number.)

The prime factors of 2401 are $\{7\}$.
The prime factors of 330 are $\{2, 3, 5, 11\}$.
The prime factors of 339 are $\{3, 113\}$.

There are no prime factors that are common to all three numbers.
When there are no common prime factors other than 1, the HCF is 1.

The HCF of $2401, 330,$ and 339 is 1.

$$\text{HCF}(2401, 330, 339) = \boxed{1}$$