The Sherwood number (Sh) is a dimensionless quantity used in heat and mass transfer analysis. It relates the rate of mass transfer between a solid surface and a fluid to the driving force for mass transfer. The Sherwood number is defined as the ratio of convective mass transfer to molecular diffusion and is given by the equation:

Sh = hL/D

where:
- Sh is the Sherwood number
- h is the convective mass transfer coefficient
- L is a characteristic length scale
- D is the diffusion coefficient

To understand the factors that influence the Sherwood number, let's consider the equation for the convective mass transfer coefficient (h):

h = k/L

where:
- h is the convective mass transfer coefficient
- k is the mass transfer coefficient
- L is a characteristic length scale

From this equation, we can see that the convective mass transfer coefficient is inversely proportional to the characteristic length scale. This means that as the length scale decreases, the convective mass transfer coefficient increases.

Now, let's consider the equation for the mass transfer coefficient (k):

k = D/δ

where:
- k is the mass transfer coefficient
- D is the diffusion coefficient
- δ is the thickness of the boundary layer

From this equation, we can see that the mass transfer coefficient is inversely proportional to the thickness of the boundary layer. This means that as the boundary layer thickness decreases, the mass transfer coefficient increases.

From the above analysis, we can conclude that the Sherwood number is influenced by the following factors:
1. Convective mass transfer coefficient (h): This is influenced by the characteristic length scale (L).
2. Mass transfer coefficient (k): This is influenced by the diffusion coefficient (D) and the thickness of the boundary layer (δ).

Therefore, the Sherwood number is a function of the Reynolds number (Re) and the Schmidt number (Sc), which are dimensionless quantities representing the ratio of inertial forces to viscous forces and the ratio of momentum diffusivity to mass diffusivity, respectively. The Reynolds number is related to the characteristic length scale and the velocity of the fluid, while the Schmidt number is related to the diffusion coefficient and the viscosity of the fluid. Hence, the correct answer is option 'C' - Reynolds number and Schmidt number.