Question

Solve this:
Q. The number of prime factors of $(3\times 5{)}^{12}(2\times 7{)}^{10}(10{)}^{25}$ is :
(A) 47
(B) 60
(C) 72
(D) 94

Answer 1

Hi,
(3 x 5)¹² x (2 x 7)¹⁰ x (10)²⁵ = (3 x 5)¹² x (2 x 7)¹⁰ x (2 x 5)²⁵

= 3¹² x 5¹² x 2¹⁰ x 7¹⁰ x 2²⁵ x 5²⁵

= 2³⁵ x 3¹² x 5³⁷ x 7¹⁰

Total number of prime factors = (35 + 12 + 37 + 10) = 94