Question

if $n$ is the number of positive integral solution of $x_1{x}_2{x}_3{x}_4=770$ then the value of $n$ is

• A. $250$
• B. $252$
• C. $254$
• D. $256$

Answer 1

The correct option is D

$256$

Explanation for correct option

Prime factorization of $770=2x5x7x11$

We can assign $2$ to $x_1$ or $x_2$ or $x_3$ or $x_4$​
Thus $2$ can be assigned in $4$ ways. Similarly each of $5,7,11$ can be assigned in $4$ ways.

Therefore, number of positive integral solution, $N=4^4=2^8=256$

Hence, option D is correct.