# Q: What is the prime factorization of the number 9,227,466?

A:
• The prime factors are: 2 x 3 x 3 x 3 x 107 x 1,597
• or also written as { 2, 3, 3, 3, 107, 1,597 }
• Written in exponential form: 21 x 33 x 1071 x 1,5971

## Why is the prime factorization of 9,227,466 written as 21 x 33 x 1071 x 1,5971?

### 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 9,227,466

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 9,227,466 by 2

9,227,466 ÷ 2 = 4,613,733 - No remainder! 2 is one of the factors!
4,613,733 ÷ 2 = 2,306,866.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
4,613,733 ÷ 3 = 1,537,911 - No remainder! 3 is one of the factors!
1,537,911 ÷ 3 = 512,637 - No remainder! 3 is one of the factors!
512,637 ÷ 3 = 170,879 - No remainder! 3 is one of the factors!
170,879 ÷ 3 = 56,959.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
170,879 ÷ 5 = 34,175.8 - This has a remainder. 5 is not a factor.
170,879 ÷ 7 = 24,411.2857 - This has a remainder. 7 is not a factor.
170,879 ÷ 11 = 15,534.4545 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
170,879 ÷ 107 = 1,597 - No remainder! 107 is one of the factors!
1,597 ÷ 107 = 14.9252 - There is a remainder. We can't divide by 107 evenly anymore. Let's try the next prime number
1,597 ÷ 109 = 14.6514 - This has a remainder. 109 is not a factor.
1,597 ÷ 113 = 14.1327 - This has a remainder. 113 is not a factor.
1,597 ÷ 127 = 12.5748 - This has a remainder. 127 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,597 ÷ 1,597 = 1 - No remainder! 1,597 is one of the factors!

The orange divisor(s) above are the prime factors of the number 9,227,466. If we put all of it together we have the factors 2 x 3 x 3 x 3 x 107 x 1,597 = 9,227,466. It can also be written in exponential form as 21 x 33 x 1071 x 1,5971.

### Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 9,227,466.

 9,227,466 2 4,613,733 3 1,537,911 3 512,637 3 170,879 107 1,597

### More Prime Factorization Examples

 9,227,464 9,227,465 9,227,467 9,227,468 23 x 171 x 191 x 3,5711 51 x 131 x 141,9611 371 x 1131 x 2,2071 22 x 2,306,8671

Try the factor calculator

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