Q: What is the prime factorization of the number 132,030?

 A:
  • The prime factors are: 2 x 3 x 3 x 3 x 3 x 5 x 163
    • or also written as { 2, 3, 3, 3, 3, 5, 163 }
  • Written in exponential form: 21 x 34 x 51 x 1631

Why is the prime factorization of 132,030 written as 21 x 34 x 51 x 1631?

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 132,030

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 132,030 by 2

132,030 ÷ 2 = 66,015 - No remainder! 2 is one of the factors!
66,015 ÷ 2 = 33,007.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
66,015 ÷ 3 = 22,005 - No remainder! 3 is one of the factors!
22,005 ÷ 3 = 7,335 - No remainder! 3 is one of the factors!
7,335 ÷ 3 = 2,445 - No remainder! 3 is one of the factors!
2,445 ÷ 3 = 815 - No remainder! 3 is one of the factors!
815 ÷ 3 = 271.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
815 ÷ 5 = 163 - No remainder! 5 is one of the factors!
163 ÷ 5 = 32.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
163 ÷ 7 = 23.2857 - This has a remainder. 7 is not a factor.
163 ÷ 11 = 14.8182 - This has a remainder. 11 is not a factor.
163 ÷ 13 = 12.5385 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
163 ÷ 163 = 1 - No remainder! 163 is one of the factors!

The orange divisor(s) above are the prime factors of the number 132,030. If we put all of it together we have the factors 2 x 3 x 3 x 3 x 3 x 5 x 163 = 132,030. It can also be written in exponential form as 21 x 34 x 51 x 1631.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 132,030.

132,030
Factor Arrows
266,015
Factor Arrows
322,005
Factor Arrows
37,335
Factor Arrows
32,445
Factor Arrows
3815
Factor Arrows
5163

More Prime Factorization Examples

132,028132,029132,031132,032
22 x 131 x 2,5391311 x 4,2591191 x 6,949126 x 2,0631

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