Q: What is the prime factorization of the number 57,884,814?

 A:
  • The prime factors are: 2 x 3 x 3 x 3 x 13 x 82,457
    • or also written as { 2, 3, 3, 3, 13, 82,457 }
  • Written in exponential form: 21 x 33 x 131 x 82,4571

Why is the prime factorization of 57,884,814 written as 21 x 33 x 131 x 82,4571?

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 57,884,814

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 57,884,814 by 2

57,884,814 ÷ 2 = 28,942,407 - No remainder! 2 is one of the factors!
28,942,407 ÷ 2 = 14,471,203.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
28,942,407 ÷ 3 = 9,647,469 - No remainder! 3 is one of the factors!
9,647,469 ÷ 3 = 3,215,823 - No remainder! 3 is one of the factors!
3,215,823 ÷ 3 = 1,071,941 - No remainder! 3 is one of the factors!
1,071,941 ÷ 3 = 357,313.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,071,941 ÷ 5 = 214,388.2 - This has a remainder. 5 is not a factor.
1,071,941 ÷ 7 = 153,134.4286 - This has a remainder. 7 is not a factor.
1,071,941 ÷ 11 = 97,449.1818 - This has a remainder. 11 is not a factor.
1,071,941 ÷ 13 = 82,457 - No remainder! 13 is one of the factors!
82,457 ÷ 13 = 6,342.8462 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
82,457 ÷ 17 = 4,850.4118 - This has a remainder. 17 is not a factor.
82,457 ÷ 19 = 4,339.8421 - This has a remainder. 19 is not a factor.
82,457 ÷ 23 = 3,585.087 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
82,457 ÷ 82,457 = 1 - No remainder! 82,457 is one of the factors!

The orange divisor(s) above are the prime factors of the number 57,884,814. If we put all of it together we have the factors 2 x 3 x 3 x 3 x 13 x 82,457 = 57,884,814. It can also be written in exponential form as 21 x 33 x 131 x 82,4571.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 57,884,814.

57,884,814
Factor Arrows
228,942,407
Factor Arrows
39,647,469
Factor Arrows
33,215,823
Factor Arrows
31,071,941
Factor Arrows
1382,457

More Prime Factorization Examples

57,884,81257,884,81357,884,81557,884,816
22 x 291 x 311 x 16,097171 x 171 x 231 x 21,149151 x 1131 x 102,451124 x 111 x 328,8911

Try the factor calculator

Explore more about the number 57,884,814:


Ask a Question