# Q: What is the prime factorization of the number 14,930,352?

A:
• The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17 x 19 x 107
• or also written as { 2, 2, 2, 2, 3, 3, 3, 17, 19, 107 }
• Written in exponential form: 24 x 33 x 171 x 191 x 1071

## Why is the prime factorization of 14,930,352 written as 24 x 33 x 171 x 191 x 1071?

### What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

### Finding the prime factors of 14,930,352

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

#### If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 14,930,352 by 2

14,930,352 ÷ 2 = 7,465,176 - No remainder! 2 is one of the factors!
7,465,176 ÷ 2 = 3,732,588 - No remainder! 2 is one of the factors!
3,732,588 ÷ 2 = 1,866,294 - No remainder! 2 is one of the factors!
1,866,294 ÷ 2 = 933,147 - No remainder! 2 is one of the factors!
933,147 ÷ 2 = 466,573.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
933,147 ÷ 3 = 311,049 - No remainder! 3 is one of the factors!
311,049 ÷ 3 = 103,683 - No remainder! 3 is one of the factors!
103,683 ÷ 3 = 34,561 - No remainder! 3 is one of the factors!
34,561 ÷ 3 = 11,520.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
34,561 ÷ 5 = 6,912.2 - This has a remainder. 5 is not a factor.
34,561 ÷ 7 = 4,937.2857 - This has a remainder. 7 is not a factor.
34,561 ÷ 11 = 3,141.9091 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
34,561 ÷ 17 = 2,033 - No remainder! 17 is one of the factors!
2,033 ÷ 17 = 119.5882 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
2,033 ÷ 19 = 107 - No remainder! 19 is one of the factors!
107 ÷ 19 = 5.6316 - There is a remainder. We can't divide by 19 evenly anymore. Let's try the next prime number
107 ÷ 23 = 4.6522 - This has a remainder. 23 is not a factor.
107 ÷ 29 = 3.6897 - This has a remainder. 29 is not a factor.
107 ÷ 31 = 3.4516 - This has a remainder. 31 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
107 ÷ 107 = 1 - No remainder! 107 is one of the factors!

The orange divisor(s) above are the prime factors of the number 14,930,352. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17 x 19 x 107 = 14,930,352. It can also be written in exponential form as 24 x 33 x 171 x 191 x 1071.

### Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 14,930,352.

 14,930,352 2 7,465,176 2 3,732,588 2 1,866,294 2 933,147 3 311,049 3 103,683 3 34,561 17 2,033 19 107

### More Prime Factorization Examples

 14,930,350 14,930,351 14,930,353 14,930,354 21 x 52 x 298,6071 371 x 1131 x 3,5711 1,5971 x 9,3491 21 x 1,7771 x 4,2011

Try the factor calculator

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