Q: What is the prime factorization of the number 131,233,331?

 A:
  • The prime factors are: 23 x 461 x 12,377
    • or also written as { 23, 461, 12,377 }
  • Written in exponential form: 231 x 4611 x 12,3771

Why is the prime factorization of 131,233,331 written as 231 x 4611 x 12,3771?

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 131,233,331

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 131,233,331 by 2

131,233,331 ÷ 2 = 65,616,665.5 - This has a remainder. Let's try another prime number.
131,233,331 ÷ 3 = 43,744,443.6667 - This has a remainder. Let's try another prime number.
131,233,331 ÷ 5 = 26,246,666.2 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
131,233,331 ÷ 23 = 5,705,797 - No remainder! 23 is one of the factors!
5,705,797 ÷ 23 = 248,078.1304 - There is a remainder. We can't divide by 23 evenly anymore. Let's try the next prime number
5,705,797 ÷ 29 = 196,751.6207 - This has a remainder. 29 is not a factor.
5,705,797 ÷ 31 = 184,057.9677 - This has a remainder. 31 is not a factor.
5,705,797 ÷ 37 = 154,210.7297 - This has a remainder. 37 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
5,705,797 ÷ 461 = 12,377 - No remainder! 461 is one of the factors!
12,377 ÷ 461 = 26.8482 - There is a remainder. We can't divide by 461 evenly anymore. Let's try the next prime number
12,377 ÷ 463 = 26.7322 - This has a remainder. 463 is not a factor.
12,377 ÷ 467 = 26.5032 - This has a remainder. 467 is not a factor.
12,377 ÷ 479 = 25.8392 - This has a remainder. 479 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
12,377 ÷ 12,377 = 1 - No remainder! 12,377 is one of the factors!

The orange divisor(s) above are the prime factors of the number 131,233,331. If we put all of it together we have the factors 23 x 461 x 12,377 = 131,233,331. It can also be written in exponential form as 231 x 4611 x 12,3771.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 131,233,331.

131,233,331
Factor Arrows
235,705,797
Factor Arrows
46112,377

More Prime Factorization Examples

131,233,329131,233,330131,233,332131,233,333
32 x 1,4231 x 10,247121 x 51 x 1032 x 1,237122 x 31 x 10,936,111171 x 112 x 411 x 3,7791

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