Number of prime factors of (3 × 5) × 12 × (2 × 7) × 10 × (10) × 25

Prime factors can simply be treated as a factor of a number which is a prime number.
Now, the above given equation is

(3 × 5) × 12 × (2 × 7) × 10 × (10) × 25×

When written in terms of prime factor it can be written as

= 3 × 5 × 6 × 2 × 2 × 7 × 2 × 5 × 2 × 5 × 5 × 5

= 3 × 5 × 3 × 2 × 2 × 2 × 7 × 2 × 5 × 2 × 5 × 5 × 5

= 2⁵ × 3² × 5⁵ × 7.

∴ There are 4 prime factors i.e. 2,3,5,7.