Question

If $N$ is the number of positive integral solutions of $x_1{x}_2{x}_3{x}_4=770$, then $N=$

• A. 256
• B. 729
• C. 292
• D. 770

Answer 1

The correct option is A 256

First factorise 770.
$770=2\times 5\times 7\times 11$
We have, $x_1\times x_2\times x_3\times x_4=770$
There are four prime factors of 770. Each of the prime factors can go to any of the four numbers.
For example - If $2$ goes to $x_1$, 5 goes to $x_2$, $7$ goes to $x_2$ and $11$ goes to $x_4$, then $x_1=2,x_2=35,x_3=1$ and $x_4=11$

Similarly each of the 4 prime numbers have 4 numbers to go to. Hence, the total number of solutions is equal to
$4\times 4\times 4\times 4=256$