Q: What is the prime factorization of the number 30,132,250?

 A:
  • The prime factors are: 2 x 5 x 5 x 5 x 43 x 2,803
    • or also written as { 2, 5, 5, 5, 43, 2,803 }
  • Written in exponential form: 21 x 53 x 431 x 2,8031

Why is the prime factorization of 30,132,250 written as 21 x 53 x 431 x 2,8031?

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 30,132,250

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 30,132,250 by 2

30,132,250 ÷ 2 = 15,066,125 - No remainder! 2 is one of the factors!
15,066,125 ÷ 2 = 7,533,062.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
15,066,125 ÷ 3 = 5,022,041.6667 - This has a remainder. 3 is not a factor.
15,066,125 ÷ 5 = 3,013,225 - No remainder! 5 is one of the factors!
3,013,225 ÷ 5 = 602,645 - No remainder! 5 is one of the factors!
602,645 ÷ 5 = 120,529 - No remainder! 5 is one of the factors!
120,529 ÷ 5 = 24,105.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
120,529 ÷ 7 = 17,218.4286 - This has a remainder. 7 is not a factor.
120,529 ÷ 11 = 10,957.1818 - This has a remainder. 11 is not a factor.
120,529 ÷ 13 = 9,271.4615 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
120,529 ÷ 43 = 2,803 - No remainder! 43 is one of the factors!
2,803 ÷ 43 = 65.186 - There is a remainder. We can't divide by 43 evenly anymore. Let's try the next prime number
2,803 ÷ 47 = 59.6383 - This has a remainder. 47 is not a factor.
2,803 ÷ 53 = 52.8868 - This has a remainder. 53 is not a factor.
2,803 ÷ 59 = 47.5085 - This has a remainder. 59 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,803 ÷ 2,803 = 1 - No remainder! 2,803 is one of the factors!

The orange divisor(s) above are the prime factors of the number 30,132,250. If we put all of it together we have the factors 2 x 5 x 5 x 5 x 43 x 2,803 = 30,132,250. It can also be written in exponential form as 21 x 53 x 431 x 2,8031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 30,132,250.

30,132,250
Factor Arrows
215,066,125
Factor Arrows
53,013,225
Factor Arrows
5602,645
Factor Arrows
5120,529
Factor Arrows
432,803

More Prime Factorization Examples

30,132,24830,132,24930,132,25130,132,252
23 x 311 x 121,501131 x 71 x 531 x 27,073130,132,251122 x 32 x 191 x 44,0531

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