Q: What is the prime factorization of the number 505,414,759?

Why is the prime factorization of 505,414,759 written as 12,967¹ x 38,977¹?

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 505,414,759

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.

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 505,414,759 by 2

505,414,759 ÷ 2 = 252,707,379.5 - This has a remainder. Let's try another prime number.
505,414,759 ÷ 3 = 168,471,586.3333 - This has a remainder. Let's try another prime number.
505,414,759 ÷ 5 = 101,082,951.8 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
505,414,759 ÷ 12,967 = 38,977 - No remainder! 12,967 is one of the factors!
38,977 ÷ 12,967 = 3.0059 - There is a remainder. We can't divide by 12967 evenly anymore. Let's try the next prime number
38,977 ÷ 12,973 = 3.0045 - This has a remainder. 12,973 is not a factor.
38,977 ÷ 12,979 = 3.0031 - This has a remainder. 12,979 is not a factor.
38,977 ÷ 12,983 = 3.0022 - This has a remainder. 12,983 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
38,977 ÷ 38,977 = 1 - No remainder! 38,977 is one of the factors!

The orange divisor(s) above are the prime factors of the number 505,414,759. If we put all of it together we have the factors 12,967 x 38,977 = 505,414,759. It can also be written in exponential form as 12,967¹ x 38,977¹.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 505,414,759.

	505,414,759
12,967		38,977

More Prime Factorization Examples

Try the factor calculator