If N is the number of positive integral solutions of x1 x2 x3 x4 = 770. Then,

We have 770 = 2 × 5 × 7 × 11. We can assign 2 to x1 or x2 or x3 or x4. That is 2 can be assigned in 4 ways.Similarly, each of 5, 7 or 11 can be assigned in 4 ways. Thus, the number of positive integral solutions ofx1 x2 x3 x4 = 770 is 44= 256