If n is a natural number and n = $${p_1}^{{x_1}}$$   $${p_2}^{{x_2}}$$   $${p_3}^{{x_3}}$$ where p₁, p₂, p₃ are distinct prime factors, then the number of prime factors for n is :

A. $${x_1} + {x_2} + {x_3}$$

B. $${x_1} \times {x_2} \times {x_3}$$

C. $$\left( {{x_1} + 1} \right)\left( {{x_2} + 1} \right)\left( {{x_3} + 1} \right)$$

D. None of these

Answer: Option B

Solution(By Examveda Team)

Given n = $${p_1}^{{x_1}}{p_2}^{{x_2}}{p_3}^{{x_3}}$$
Where p₁, p₂, p₃ are distinct prime factors
Number of prime factors form :
= (x₁ × x₂ × x₃)
= x₁ x₂ x₃
Hence option (B) is correct