The number of ways in which 900 can be resolved as a product of two factors is 

$$\begin{gathered} \boxed{\text{ The number of ways in which }\mathrm{N}\text{ can be resolved as a product of two factors } \\ \frac{\left({\mathrm{\alpha }}_1+1\right)\left({\mathrm{\alpha }}_2+1\right)\dots \dots \left({\mathrm{\alpha }}_{\mathrm{k}}+1\right)}{2}\left(\mathrm{N}\text{ is not a perfect square }\right) \\ \frac{\left({\mathrm{\alpha }}_1+1\right)\left({\mathrm{\alpha }}_2+1\right)\dots ..\left({\mathrm{\alpha }}_{\mathrm{k}}+1\right)+1}{2}\left(\mathrm{N}\text{ is a perfect square }\right)} \end{gathered}$$$900=2^2\times 3^2\times 5^2$

Total no of divisors = (2+1) (2+1) (2+1)

                                   = 27

No of ways 900  is divided into product of 2 factors $=\frac{27+1}{2}=14$