Correct Option: A

We break each base number into prime factors.
Now, 307= (2 × 3 × 5)⁷= 2⁷ × 3⁷ × 5⁷
22⁵ = (2 × 11)⁵ = 2⁵ × 11⁵
34¹² = (2 × 17)¹² = 2¹² × 17¹²
12⁵ = (3 × 2 × 2)⁵ = 3⁵ × 2⁵ × 2⁵
∴  30⁷ × 2² × 34¹² × 12⁵ = 2⁷ × 3⁷ × 5⁷ × 2⁵ × 11⁵ × 2¹² × 17¹² × 3⁵ × 2⁵ × 2⁵
= 2^7+5+12+5+5 × 3⁷⁺⁵ × 5⁷ × 11⁵ × 17¹²
= 2³⁴ × 3¹² × 5⁷ × 11⁵ × 17¹²
∴  The required number of prime factors
= 34 + 12 + 7 + 5 + 12 = 70