Correct Answer - Option 4 : C

**Given:**

Product = { (8)10 × (9)7 × 78 }

**Concept:**

The prime number are numbers that have only 2 factors:1 and themselves.

Prime factors

**Calculation:**

8 = 2 × 2 × 2 = 2^{3} ----(i)

9 = 3 × 3 ----(ii)

7 = 7^{1} ----(iii)

Substituting (i) (ii) (iii) in the equation

{ (8)10 × (9)7 × 78 } = 2^{(3 × 10)} × 3^{(2 × 7)} × 7^{8} = 2^{30} × 3^{14} × 7^{8}

2, 3, 7 are the prime numbers

Powers represent the number of prime numbers

equating and adding the powers of all prime number

30 + 14 + 8 = 52

**∴ The total prime factors in the product of { (8)10 × (9)7 × 78 } is 52**