Q: What is the prime factorization of the number 22,815?

 A:
  • The prime factors are: 3 x 3 x 3 x 5 x 13 x 13
    • or also written as { 3, 3, 3, 5, 13, 13 }
  • Written in exponential form: 33 x 51 x 132

Why is the prime factorization of 22,815 written as 33 x 51 x 132?

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 22,815

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 22,815 by 2

22,815 ÷ 2 = 11,407.5 - This has a remainder. Let's try another prime number.
22,815 ÷ 3 = 7,605 - No remainder! 3 is one of the factors!
7,605 ÷ 3 = 2,535 - No remainder! 3 is one of the factors!
2,535 ÷ 3 = 845 - No remainder! 3 is one of the factors!
845 ÷ 3 = 281.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
845 ÷ 5 = 169 - No remainder! 5 is one of the factors!
169 ÷ 5 = 33.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
169 ÷ 7 = 24.1429 - This has a remainder. 7 is not a factor.
169 ÷ 11 = 15.3636 - This has a remainder. 11 is not a factor.
169 ÷ 13 = 13 - No remainder! 13 is one of the factors!
13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 22,815. If we put all of it together we have the factors 3 x 3 x 3 x 5 x 13 x 13 = 22,815. It can also be written in exponential form as 33 x 51 x 132.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 22,815.

22,815
Factor Arrows
37,605
Factor Arrows
32,535
Factor Arrows
3845
Factor Arrows
5169
Factor Arrows
1313

More Prime Factorization Examples

22,81322,81422,81622,817
71 x 3,259121 x 111 x 171 x 61125 x 231 x 31122,8171

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