Find the remainder when 496 is divided by 6.

Answer: Option D

$$\frac{4^{96}}{6},$$ we can write it in this form
$$\frac{{\left(6-2\right)}^{96}}{6}$$
Now, Remainder will depend only the powers of -2. So,
$$\frac{{\left(-2\right)}^{96}}{6},$$   it is same as
$$\frac{{\left({\left[-2\right]}^4\right)}^{24}}{6},$$   it is same as
$$\frac{{\left(16\right)}^{24}}{6}$$
Now,
$$\frac{\left(16\times 16\times 16\times 16......24\text{times}\right)}{6}$$
On dividing individually 16 we always get a remainder 4.
$$\frac{\left(4\times 4\times 4\times 4......24\text{times}\right)}{6}$$
Hence, Required Remainder = 4
NOTE: When 4 has even number of powers, it will always give remainder 4 on dividing by 6.