Q: What is the prime factorization of the number 300,055,720?

 A:
  • The prime factors are: 2 x 2 x 2 x 5 x 43 x 43 x 4,057
    • or also written as { 2, 2, 2, 5, 43, 43, 4,057 }
  • Written in exponential form: 23 x 51 x 432 x 4,0571

Why is the prime factorization of 300,055,720 written as 23 x 51 x 432 x 4,0571?

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 300,055,720

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 300,055,720 by 2

300,055,720 ÷ 2 = 150,027,860 - No remainder! 2 is one of the factors!
150,027,860 ÷ 2 = 75,013,930 - No remainder! 2 is one of the factors!
75,013,930 ÷ 2 = 37,506,965 - No remainder! 2 is one of the factors!
37,506,965 ÷ 2 = 18,753,482.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
37,506,965 ÷ 3 = 12,502,321.6667 - This has a remainder. 3 is not a factor.
37,506,965 ÷ 5 = 7,501,393 - No remainder! 5 is one of the factors!
7,501,393 ÷ 5 = 1,500,278.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
7,501,393 ÷ 7 = 1,071,627.5714 - This has a remainder. 7 is not a factor.
7,501,393 ÷ 11 = 681,944.8182 - This has a remainder. 11 is not a factor.
7,501,393 ÷ 13 = 577,030.2308 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
7,501,393 ÷ 43 = 174,451 - No remainder! 43 is one of the factors!
174,451 ÷ 43 = 4,057 - No remainder! 43 is one of the factors!
4,057 ÷ 43 = 94.3488 - There is a remainder. We can't divide by 43 evenly anymore. Let's try the next prime number
4,057 ÷ 47 = 86.3191 - This has a remainder. 47 is not a factor.
4,057 ÷ 53 = 76.5472 - This has a remainder. 53 is not a factor.
4,057 ÷ 59 = 68.7627 - This has a remainder. 59 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
4,057 ÷ 4,057 = 1 - No remainder! 4,057 is one of the factors!

The orange divisor(s) above are the prime factors of the number 300,055,720. If we put all of it together we have the factors 2 x 2 x 2 x 5 x 43 x 43 x 4,057 = 300,055,720. It can also be written in exponential form as 23 x 51 x 432 x 4,0571.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 300,055,720.

300,055,720
Factor Arrows
2150,027,860
Factor Arrows
275,013,930
Factor Arrows
237,506,965
Factor Arrows
57,501,393
Factor Arrows
43174,451
Factor Arrows
434,057

More Prime Factorization Examples

300,055,718300,055,719300,055,721300,055,722
21 x 371 x 4,054,807131 x 100,018,573171 x 291 x 8291 x 1,783121 x 31 x 50,009,2871

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