Question

Find the total prime factors in the product of { (8)10 × (9)7 × 78 }.

A. 45

B. 54

C. 52

D. 65

1. B
2. A
3. D
4. C

Answer 1

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 = 2³       ----(i)

9 = 3 × 3       ----(ii)

7 = 7¹       ----(iii)

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

{ (8)10 × (9)7 × 78 } = 2^{(3 × 10)} × 3^{(2 × 7)} × 7⁸ = 2³⁰ × 3¹⁴ × 7⁸

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