Q: What is the prime factorization of the number 534,555,456?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 53 x 131 x 401
    • or also written as { 2, 2, 2, 2, 2, 2, 3, 53, 131, 401 }
  • Written in exponential form: 26 x 31 x 531 x 1311 x 4011

Why is the prime factorization of 534,555,456 written as 26 x 31 x 531 x 1311 x 4011?

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 534,555,456

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 534,555,456 by 2

534,555,456 ÷ 2 = 267,277,728 - No remainder! 2 is one of the factors!
267,277,728 ÷ 2 = 133,638,864 - No remainder! 2 is one of the factors!
133,638,864 ÷ 2 = 66,819,432 - No remainder! 2 is one of the factors!
66,819,432 ÷ 2 = 33,409,716 - No remainder! 2 is one of the factors!
33,409,716 ÷ 2 = 16,704,858 - No remainder! 2 is one of the factors!
16,704,858 ÷ 2 = 8,352,429 - No remainder! 2 is one of the factors!
8,352,429 ÷ 2 = 4,176,214.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
8,352,429 ÷ 3 = 2,784,143 - No remainder! 3 is one of the factors!
2,784,143 ÷ 3 = 928,047.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
2,784,143 ÷ 5 = 556,828.6 - This has a remainder. 5 is not a factor.
2,784,143 ÷ 7 = 397,734.7143 - This has a remainder. 7 is not a factor.
2,784,143 ÷ 11 = 253,103.9091 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,784,143 ÷ 53 = 52,531 - No remainder! 53 is one of the factors!
52,531 ÷ 53 = 991.1509 - There is a remainder. We can't divide by 53 evenly anymore. Let's try the next prime number
52,531 ÷ 59 = 890.3559 - This has a remainder. 59 is not a factor.
52,531 ÷ 61 = 861.1639 - This has a remainder. 61 is not a factor.
52,531 ÷ 67 = 784.0448 - This has a remainder. 67 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
52,531 ÷ 131 = 401 - No remainder! 131 is one of the factors!
401 ÷ 131 = 3.0611 - There is a remainder. We can't divide by 131 evenly anymore. Let's try the next prime number
401 ÷ 137 = 2.927 - This has a remainder. 137 is not a factor.
401 ÷ 139 = 2.8849 - This has a remainder. 139 is not a factor.
401 ÷ 149 = 2.6913 - This has a remainder. 149 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
401 ÷ 401 = 1 - No remainder! 401 is one of the factors!

The orange divisor(s) above are the prime factors of the number 534,555,456. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 3 x 53 x 131 x 401 = 534,555,456. It can also be written in exponential form as 26 x 31 x 531 x 1311 x 4011.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 534,555,456.

534,555,456
Factor Arrows
2267,277,728
Factor Arrows
2133,638,864
Factor Arrows
266,819,432
Factor Arrows
233,409,716
Factor Arrows
216,704,858
Factor Arrows
28,352,429
Factor Arrows
32,784,143
Factor Arrows
5352,531
Factor Arrows
131401

More Prime Factorization Examples

534,555,454534,555,455534,555,457534,555,458
21 x 10,2591 x 26,053151 x 72 x 2691 x 8,1111971 x 5,510,881121 x 411 x 591 x 110,4911

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