The correct answer is A. (i) and (iii).
The correction factor is a dimensionless quantity that is used to account for the effects of relativity on the motion of particles. It is given by the following equation:
$$\gamma = \frac{1}{\sqrt{1 – \frac{v^2}{c^2}}}$$
where $v$ is the velocity of the particle and $c$ is the speed of light.
The correction factor is always greater than or equal to 1. When $v = 0$, then $\gamma = 1$. When $v = c$, then $\gamma = \infty$.
The kinetic energy of a particle is given by the following equation:
$$E_k = \frac{1}{2}mv^2$$
where $m$ is the mass of the particle.
The momentum of a particle is given by the following equation:
$$p = mv$$
When the kinetic energy of a particle is zero, then the velocity of the particle is also zero. This means that the correction factor is also zero.
When the momentum of a particle is zero, then the velocity of the particle is not necessarily zero. This means that the correction factor is not necessarily zero.
Therefore, the least possible value of the correction factor is zero when the kinetic energy of the particle is zero. The least possible value of the correction factor is not zero when the momentum of the particle is zero.