### What is the number of prime factors contained in the product 30^{7} X 22^{5} X 34^{11 }

**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 **

**30 ^{7} X 22^{5} X 34^{11 }**

= **( 2 X 3 X 5 ) ^{7} X ( 2 X 11 )^{5} X ( 2 X 17 )^{11}**

= **2 ^{7} X 2^{5} X 2^{11}**

**X 3**

^{7}X 5^{7}X 11^{5}X 17^{11}** Apply this formula**

** [ a**^{m}** x a**^{n}** = a**^{m + n}** ] **

= **2 ^{7 + 5 + 11} X 3^{7} X 5^{7} X 11^{5} X 17^{11}**

= **2 ^{23} X 3^{7} X 5^{7} X 11^{5} X 17^{11}**

**Sum of only Powers**

** ^{ } Total Factors** :

**23 + 7 + 7 + 5 + 11**

= **53 **

#### 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**