Q: What is the prime factorization of the number 511,177,032?

 A:
  • The prime factors are: 2 x 2 x 2 x 3 x 3 x 127 x 55,903
    • or also written as { 2, 2, 2, 3, 3, 127, 55,903 }
  • Written in exponential form: 23 x 32 x 1271 x 55,9031

Why is the prime factorization of 511,177,032 written as 23 x 32 x 1271 x 55,9031?

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 511,177,032

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 511,177,032 by 2

511,177,032 ÷ 2 = 255,588,516 - No remainder! 2 is one of the factors!
255,588,516 ÷ 2 = 127,794,258 - No remainder! 2 is one of the factors!
127,794,258 ÷ 2 = 63,897,129 - No remainder! 2 is one of the factors!
63,897,129 ÷ 2 = 31,948,564.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
63,897,129 ÷ 3 = 21,299,043 - No remainder! 3 is one of the factors!
21,299,043 ÷ 3 = 7,099,681 - No remainder! 3 is one of the factors!
7,099,681 ÷ 3 = 2,366,560.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
7,099,681 ÷ 5 = 1,419,936.2 - This has a remainder. 5 is not a factor.
7,099,681 ÷ 7 = 1,014,240.1429 - This has a remainder. 7 is not a factor.
7,099,681 ÷ 11 = 645,425.5455 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
7,099,681 ÷ 127 = 55,903 - No remainder! 127 is one of the factors!
55,903 ÷ 127 = 440.1811 - There is a remainder. We can't divide by 127 evenly anymore. Let's try the next prime number
55,903 ÷ 131 = 426.7405 - This has a remainder. 131 is not a factor.
55,903 ÷ 137 = 408.0511 - This has a remainder. 137 is not a factor.
55,903 ÷ 139 = 402.1799 - This has a remainder. 139 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
55,903 ÷ 55,903 = 1 - No remainder! 55,903 is one of the factors!

The orange divisor(s) above are the prime factors of the number 511,177,032. If we put all of it together we have the factors 2 x 2 x 2 x 3 x 3 x 127 x 55,903 = 511,177,032. It can also be written in exponential form as 23 x 32 x 1271 x 55,9031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 511,177,032.

511,177,032
Factor Arrows
2255,588,516
Factor Arrows
2127,794,258
Factor Arrows
263,897,129
Factor Arrows
321,299,043
Factor Arrows
37,099,681
Factor Arrows
12755,903

More Prime Factorization Examples

511,177,030511,177,031511,177,033511,177,034
21 x 51 x 71 x 131 x 561,73316,0791 x 84,08912,5511 x 200,383121 x 431 x 5,943,9191

Try the factor calculator

Explore more about the number 511,177,032:


Ask a Question