The total number of 4-digit numbers whose greatest common divisor with $$54$$ is $$2$$, is

Find the total number of 4-digit numbers whose GCD with 54 is 2.

$$54 = 2 \times 3^3$$

$$\gcd(n, 54) = 2$$ means:

- $$n$$ is divisible by 2 (even), and

- $$\gcd(n, 27) = 1$$, i.e., $$n$$ is not divisible by 3.

4-digit numbers range from 1000 to 9999. Total = 9000.

Even 4-digit numbers: $$\frac{9000}{2} = 4500$$

Multiples of 6 from 1000 to 9999: $$\lfloor 9999/6 \rfloor - \lfloor 999/6 \rfloor = 1666 - 166 = 1500$$

Count = $$4500 - 1500 = 3000$$

The answer is $$\boxed{3000}$$.