Q: What is the prime factorization of the number 314,320,032?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 37 x 2,269
    • or also written as { 2, 2, 2, 2, 2, 3, 3, 13, 37, 2,269 }
  • Written in exponential form: 25 x 32 x 131 x 371 x 2,2691

Why is the prime factorization of 314,320,032 written as 25 x 32 x 131 x 371 x 2,2691?

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 314,320,032

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 314,320,032 by 2

314,320,032 ÷ 2 = 157,160,016 - No remainder! 2 is one of the factors!
157,160,016 ÷ 2 = 78,580,008 - No remainder! 2 is one of the factors!
78,580,008 ÷ 2 = 39,290,004 - No remainder! 2 is one of the factors!
39,290,004 ÷ 2 = 19,645,002 - No remainder! 2 is one of the factors!
19,645,002 ÷ 2 = 9,822,501 - No remainder! 2 is one of the factors!
9,822,501 ÷ 2 = 4,911,250.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
9,822,501 ÷ 3 = 3,274,167 - No remainder! 3 is one of the factors!
3,274,167 ÷ 3 = 1,091,389 - No remainder! 3 is one of the factors!
1,091,389 ÷ 3 = 363,796.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,091,389 ÷ 5 = 218,277.8 - This has a remainder. 5 is not a factor.
1,091,389 ÷ 7 = 155,912.7143 - This has a remainder. 7 is not a factor.
1,091,389 ÷ 11 = 99,217.1818 - This has a remainder. 11 is not a factor.
1,091,389 ÷ 13 = 83,953 - No remainder! 13 is one of the factors!
83,953 ÷ 13 = 6,457.9231 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
83,953 ÷ 17 = 4,938.4118 - This has a remainder. 17 is not a factor.
83,953 ÷ 19 = 4,418.5789 - This has a remainder. 19 is not a factor.
83,953 ÷ 23 = 3,650.1304 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
83,953 ÷ 37 = 2,269 - No remainder! 37 is one of the factors!
2,269 ÷ 37 = 61.3243 - There is a remainder. We can't divide by 37 evenly anymore. Let's try the next prime number
2,269 ÷ 41 = 55.3415 - This has a remainder. 41 is not a factor.
2,269 ÷ 43 = 52.7674 - This has a remainder. 43 is not a factor.
2,269 ÷ 47 = 48.2766 - This has a remainder. 47 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,269 ÷ 2,269 = 1 - No remainder! 2,269 is one of the factors!

The orange divisor(s) above are the prime factors of the number 314,320,032. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 37 x 2,269 = 314,320,032. It can also be written in exponential form as 25 x 32 x 131 x 371 x 2,2691.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 314,320,032.

314,320,032
Factor Arrows
2157,160,016
Factor Arrows
278,580,008
Factor Arrows
239,290,004
Factor Arrows
219,645,002
Factor Arrows
29,822,501
Factor Arrows
33,274,167
Factor Arrows
31,091,389
Factor Arrows
1383,953
Factor Arrows
372,269

More Prime Factorization Examples

314,320,030314,320,031314,320,033314,320,034
21 x 51 x 1091 x 4571 x 6311314,320,03114911 x 640,163121 x 71 x 3,8531 x 5,8271

Try the factor calculator

Explore more about the number 314,320,032:


Ask a Question