Q: What is the prime factorization of the number 64,288,027?

 A:
  • The prime factors are: 479 x 134,213
    • or also written as { 479, 134,213 }
  • Written in exponential form: 4791 x 134,2131

Why is the prime factorization of 64,288,027 written as 4791 x 134,2131?

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 64,288,027

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 64,288,027 by 2

64,288,027 ÷ 2 = 32,144,013.5 - This has a remainder. Let's try another prime number.
64,288,027 ÷ 3 = 21,429,342.3333 - This has a remainder. Let's try another prime number.
64,288,027 ÷ 5 = 12,857,605.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
64,288,027 ÷ 479 = 134,213 - No remainder! 479 is one of the factors!
134,213 ÷ 479 = 280.1942 - There is a remainder. We can't divide by 479 evenly anymore. Let's try the next prime number
134,213 ÷ 487 = 275.5914 - This has a remainder. 487 is not a factor.
134,213 ÷ 491 = 273.3462 - This has a remainder. 491 is not a factor.
134,213 ÷ 499 = 268.9639 - This has a remainder. 499 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
134,213 ÷ 134,213 = 1 - No remainder! 134,213 is one of the factors!

The orange divisor(s) above are the prime factors of the number 64,288,027. If we put all of it together we have the factors 479 x 134,213 = 64,288,027. It can also be written in exponential form as 4791 x 134,2131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 64,288,027.

64,288,027
Factor Arrows
479134,213

More Prime Factorization Examples

64,288,02564,288,02664,288,02864,288,029
52 x 1,2171 x 2,113121 x 33 x 112 x 9,839122 x 71 x 2,296,001131 x 131 x 1791 x 9,2091

Try the factor calculator

Explore more about the number 64,288,027:


Ask a Question