Q: What is the prime factorization of the number 323,433?

 A:
  • The prime factors are: 3 x 3 x 3 x 3 x 3 x 11 x 11 x 11
    • or also written as { 3, 3, 3, 3, 3, 11, 11, 11 }
  • Written in exponential form: 35 x 113

Why is the prime factorization of 323,433 written as 35 x 113?

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 323,433

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 323,433 by 2

323,433 ÷ 2 = 161,716.5 - This has a remainder. Let's try another prime number.
323,433 ÷ 3 = 107,811 - No remainder! 3 is one of the factors!
107,811 ÷ 3 = 35,937 - No remainder! 3 is one of the factors!
35,937 ÷ 3 = 11,979 - No remainder! 3 is one of the factors!
11,979 ÷ 3 = 3,993 - No remainder! 3 is one of the factors!
3,993 ÷ 3 = 1,331 - No remainder! 3 is one of the factors!
1,331 ÷ 3 = 443.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,331 ÷ 5 = 266.2 - This has a remainder. 5 is not a factor.
1,331 ÷ 7 = 190.1429 - This has a remainder. 7 is not a factor.
1,331 ÷ 11 = 121 - No remainder! 11 is one of the factors!
121 ÷ 11 = 11 - No remainder! 11 is one of the factors!
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

The orange divisor(s) above are the prime factors of the number 323,433. If we put all of it together we have the factors 3 x 3 x 3 x 3 x 3 x 11 x 11 x 11 = 323,433. It can also be written in exponential form as 35 x 113.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 323,433.

323,433
Factor Arrows
3107,811
Factor Arrows
335,937
Factor Arrows
311,979
Factor Arrows
33,993
Factor Arrows
31,331
Factor Arrows
11121
Factor Arrows
1111

More Prime Factorization Examples

323,431323,432323,434323,435
2811 x 1,151123 x 40,429121 x 161,717151 x 71 x 9,2411

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