If the standard deviation of 20 observations $x_1,x_2,x_3,\mathrm{.....},x_{20}$  is 4 and that of another 20 observations $y_1,y_2,y_3,\mathrm{.....},y_{20}$ is 3. Also  $X_i=(x_i-\overline{x})(y_i-\overline{y})$ where $\overline{x}and\overline{y}$ are means of ${x_i}^{\text{'}}sand{y_i}^{\text{'}}s$ respectively. If $\sum _{i=1}^{20}{X}_i=90$ , then the standard deviation of the observations $x_1-y_1,x_2-y_2,x_3-y_3,\mathrm{...........},x_{20}-y_{20}$ is divisible by