Number of positive integral solutions of x1 ⋅ x2. ⋅ x3=30 is

Question

Number of positive integral solutions of x1 ⋅ x2. ⋅ x3=30 is (A) 25 (B) 26 (C) 27 (D) 28

Tardigrade Admin · Accepted Answer

We have 30 = 2.3.5. We can assign in 2 to x1 or x2 or x3 That is 2 can be assigned in 3 ways. Similarly each of 3 and 5 can be assigned in 3 Ways. Thus the numbers of solutions = 3 × 3× 3 = 27.

Q. Number of positive integral solutions of $x_{1} \cdot x_{2} . \cdot x_{3} = 30$ is

$25$

$26$

$27$

$28$

We have $30 = 2.3.5$ . We can assign in $2$ to $x_{1}$ or $x_{2}$ or $x_{3}$ That is $2$ can be assigned in $3$ ways. Similarly each of $3$ and $5$ can be assigned in $3$ Ways. Thus the numbers of solutions $= 3 \times 3 \times 3$
$= 27$ .

Q. Number of positive integral solutions of x1​⋅x2​.⋅x3​=30 is

25

26

27

28