Q: What is the prime factorization of the number 510,551,504?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 197 x 161,977
    • or also written as { 2, 2, 2, 2, 197, 161,977 }
  • Written in exponential form: 24 x 1971 x 161,9771

Why is the prime factorization of 510,551,504 written as 24 x 1971 x 161,9771?

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 510,551,504

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 510,551,504 by 2

510,551,504 ÷ 2 = 255,275,752 - No remainder! 2 is one of the factors!
255,275,752 ÷ 2 = 127,637,876 - No remainder! 2 is one of the factors!
127,637,876 ÷ 2 = 63,818,938 - No remainder! 2 is one of the factors!
63,818,938 ÷ 2 = 31,909,469 - No remainder! 2 is one of the factors!
31,909,469 ÷ 2 = 15,954,734.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
31,909,469 ÷ 3 = 10,636,489.6667 - This has a remainder. 3 is not a factor.
31,909,469 ÷ 5 = 6,381,893.8 - This has a remainder. 5 is not a factor.
31,909,469 ÷ 7 = 4,558,495.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
31,909,469 ÷ 197 = 161,977 - No remainder! 197 is one of the factors!
161,977 ÷ 197 = 822.2183 - There is a remainder. We can't divide by 197 evenly anymore. Let's try the next prime number
161,977 ÷ 199 = 813.9548 - This has a remainder. 199 is not a factor.
161,977 ÷ 211 = 767.6635 - This has a remainder. 211 is not a factor.
161,977 ÷ 223 = 726.3543 - This has a remainder. 223 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
161,977 ÷ 161,977 = 1 - No remainder! 161,977 is one of the factors!

The orange divisor(s) above are the prime factors of the number 510,551,504. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 197 x 161,977 = 510,551,504. It can also be written in exponential form as 24 x 1971 x 161,9771.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 510,551,504.

510,551,504
Factor Arrows
2255,275,752
Factor Arrows
2127,637,876
Factor Arrows
263,818,938
Factor Arrows
231,909,469
Factor Arrows
197161,977

More Prime Factorization Examples

510,551,502510,551,503510,551,505510,551,506
21 x 31 x 85,091,917171 x 111 x 6,630,539136 x 51 x 140,069121 x 471 x 5,431,3991

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