Question

If a number is in the form of $8^{10} \times9^7\times7^8$, find the total number of prime factors of the given number.

• A. 52
• B. 560
• C. 3360
• D. 25

Answer 1

Answer:

A. 52

Given:

The number is 8¹⁰ $\times$ 9⁷ $\times$ 7⁸ 

Concept used:

If a number of the form x^a $\times$ y^b $\times$ z^c ...... and so on, then total prime factors = a + b + c ..... and so on

Where x, y, z, ... are prime numbers

Calculation:

The number 8¹⁰ $\times$ 9⁷ $\times$ 7⁸ can be written as (2³)¹⁰ $\times$ (3²)⁷ $\times$ 7⁸ 

The number can ve written as 2³⁰ $\times$ 3¹⁴ $\times$ 7⁸ 

Total number of prime factors = 30 + 14 + 8

∴ The total number of prime factors are 52