Q: What is the prime factorization of the number 200,730,368?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 784,103
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 784,103 }
  • Written in exponential form: 28 x 784,1031

Why is the prime factorization of 200,730,368 written as 28 x 784,1031?

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 200,730,368

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 200,730,368 by 2

200,730,368 ÷ 2 = 100,365,184 - No remainder! 2 is one of the factors!
100,365,184 ÷ 2 = 50,182,592 - No remainder! 2 is one of the factors!
50,182,592 ÷ 2 = 25,091,296 - No remainder! 2 is one of the factors!
25,091,296 ÷ 2 = 12,545,648 - No remainder! 2 is one of the factors!
12,545,648 ÷ 2 = 6,272,824 - No remainder! 2 is one of the factors!
6,272,824 ÷ 2 = 3,136,412 - No remainder! 2 is one of the factors!
3,136,412 ÷ 2 = 1,568,206 - No remainder! 2 is one of the factors!
1,568,206 ÷ 2 = 784,103 - No remainder! 2 is one of the factors!
784,103 ÷ 2 = 392,051.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
784,103 ÷ 3 = 261,367.6667 - This has a remainder. 3 is not a factor.
784,103 ÷ 5 = 156,820.6 - This has a remainder. 5 is not a factor.
784,103 ÷ 7 = 112,014.7143 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
784,103 ÷ 784,103 = 1 - No remainder! 784,103 is one of the factors!

The orange divisor(s) above are the prime factors of the number 200,730,368. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 784,103 = 200,730,368. It can also be written in exponential form as 28 x 784,1031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 200,730,368.

200,730,368
Factor Arrows
2100,365,184
Factor Arrows
250,182,592
Factor Arrows
225,091,296
Factor Arrows
212,545,648
Factor Arrows
26,272,824
Factor Arrows
23,136,412
Factor Arrows
21,568,206
Factor Arrows
2784,103

More Prime Factorization Examples

200,730,366200,730,367200,730,369200,730,370
21 x 33 x 7431 x 5,00311091 x 1,3071 x 1,409131 x 71 x 9,558,589121 x 51 x 1,6071 x 12,4911

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