# Q: What is the prime factorization of the number 9,227,467?

A:
• The prime factors are: 37 x 113 x 2,207
• or also written as { 37, 113, 2,207 }
• Written in exponential form: 371 x 1131 x 2,2071

## Why is the prime factorization of 9,227,467 written as 371 x 1131 x 2,2071?

### 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 9,227,467

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 9,227,467 by 2

9,227,467 ÷ 2 = 4,613,733.5 - This has a remainder. Let's try another prime number.
9,227,467 ÷ 3 = 3,075,822.3333 - This has a remainder. Let's try another prime number.
9,227,467 ÷ 5 = 1,845,493.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
9,227,467 ÷ 37 = 249,391 - No remainder! 37 is one of the factors!
249,391 ÷ 37 = 6,740.2973 - There is a remainder. We can't divide by 37 evenly anymore. Let's try the next prime number
249,391 ÷ 41 = 6,082.7073 - This has a remainder. 41 is not a factor.
249,391 ÷ 43 = 5,799.7907 - This has a remainder. 43 is not a factor.
249,391 ÷ 47 = 5,306.1915 - This has a remainder. 47 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
249,391 ÷ 113 = 2,207 - No remainder! 113 is one of the factors!
2,207 ÷ 113 = 19.531 - There is a remainder. We can't divide by 113 evenly anymore. Let's try the next prime number
2,207 ÷ 127 = 17.378 - This has a remainder. 127 is not a factor.
2,207 ÷ 131 = 16.8473 - This has a remainder. 131 is not a factor.
2,207 ÷ 137 = 16.1095 - This has a remainder. 137 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,207 ÷ 2,207 = 1 - No remainder! 2,207 is one of the factors!

The orange divisor(s) above are the prime factors of the number 9,227,467. If we put all of it together we have the factors 37 x 113 x 2,207 = 9,227,467. It can also be written in exponential form as 371 x 1131 x 2,2071.

### Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 9,227,467.

 9,227,467 37 249,391 113 2,207

### More Prime Factorization Examples

 9,227,465 9,227,466 9,227,468 9,227,469 51 x 131 x 141,9611 21 x 33 x 1071 x 1,5971 22 x 2,306,8671 31 x 3891 x 7,9071

Try the factor calculator

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