What is the number of prime factors contained in the product 30⁷ × 22⁵ × 34¹¹ ?

A. 49

B. 51

C. 52

D. 53

Answer: Option D

Solution(By Examveda Team)

30⁷ × 22⁵ × 34¹¹
= (2 × 3 × 5)⁷ × (2 × 11)⁵ × (2 × 7)¹¹
= 2^{(7 + 5 + 11)} × 3⁷ × 5⁷ × 11⁵ × 17¹¹
= (2²³ × 3⁷ × 5⁷ × 11⁵ × 17¹¹)
Number of prime factors
= (23 + 7 + 7 + 5 + 11)
= 53