The Number of prime factors contained in

What is the number of prime factors contained in the product 30⁷ X 22⁵ X 34¹¹ 

The Number of Prime factors formula

A factor that is a prime number.

In other words: any of the prime numbers that can be multiplied to give the original

30⁷ X 22⁵ X 34¹¹ 

• 

= ( 2 X 3 X 5 )⁷ X ( 2 X 11 )⁵ X ( 2 X 17 )¹¹

= 2⁷ X 2⁵ X 2¹¹ X 3⁷ X 5⁷ X 11⁵ X 17¹¹

Apply this formula

[ a^m x aⁿ = a^{m + n} ]

= 2^{7 + 5 + 11} X 3⁷ X 5⁷ X 11⁵ X 17¹¹

= 2²³ X 3⁷ X 5⁷ X 11⁵ X 17¹¹

Sum of only Powers

  Total  Factors : 23 + 7 + 7 + 5 + 11

= 53

https://youtu.be/2ta0gHQySWo

for jobs click here

Total number of prime factors formula

Natural Numbers :

The numbers which are used in counting are known as Natural Numbers or Positive Integers.

There set is denoted by N. Thus, N =  { 1,2,3,4,5,6,7,8,……….. }

Whole Numbers : 

The set of whole numbers is denoted by ‘W’  Where  ‘W’ = { 0,1,2,3,4,5,6,7,8,……….. }

  Set of Integers :

All counting numbers. Their negative and ‘O’. When combined from the set of integers.  

This is denoted by I . Thus, I =  { ……-3,-2,-1,0, 1,2,3,4,5,6,7,8,……….. }

Even Numbers :

Those numbers which are exactly divisible by 2 are known as even numbers. For example  2, 4, 6, 8, ………

Odd Numbers :

The numbers which are not exactly divisible by 2 are Called Odd numbers. For example  1, 3, 5, 7, ……… are Odd Numbers

A factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original total number of prime factors formula