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
This Question Belongs to Arithmetic Ability >> Number System
Answer will be option a. x1+x2+x3