The number of positive integral solution of the equation $x_1{x}_2{x}_3{x}_4{x}_5=1050$ is 375n when $n\in N.$ Then $n=\_\_\_\_\_\_\_$

 $x_1{x}_2{x}_3{x}_4{x}_5=2\times 3\times 5^2\times 7$ we can assign 2, 3 or 7 to any of 5 variables. We can assign $5^2$ to just one variable in 5 ways or can assign $5^2=5\times 5$ to two variables in $5_{c_2}$ ways. Then 5 can be assigned in $5c_1+5c_2=5+10=15$ ways Hence required solutions $=5\times 5\times 5\times 15=1875.$