Q: What is the prime factorization of the number 52,542,432?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 29 x 233
    • or also written as { 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 29, 233 }
  • Written in exponential form: 25 x 35 x 291 x 2331

Why is the prime factorization of 52,542,432 written as 25 x 35 x 291 x 2331?

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 52,542,432

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 52,542,432 by 2

52,542,432 ÷ 2 = 26,271,216 - No remainder! 2 is one of the factors!
26,271,216 ÷ 2 = 13,135,608 - No remainder! 2 is one of the factors!
13,135,608 ÷ 2 = 6,567,804 - No remainder! 2 is one of the factors!
6,567,804 ÷ 2 = 3,283,902 - No remainder! 2 is one of the factors!
3,283,902 ÷ 2 = 1,641,951 - No remainder! 2 is one of the factors!
1,641,951 ÷ 2 = 820,975.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,641,951 ÷ 3 = 547,317 - No remainder! 3 is one of the factors!
547,317 ÷ 3 = 182,439 - No remainder! 3 is one of the factors!
182,439 ÷ 3 = 60,813 - No remainder! 3 is one of the factors!
60,813 ÷ 3 = 20,271 - No remainder! 3 is one of the factors!
20,271 ÷ 3 = 6,757 - No remainder! 3 is one of the factors!
6,757 ÷ 3 = 2,252.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
6,757 ÷ 5 = 1,351.4 - This has a remainder. 5 is not a factor.
6,757 ÷ 7 = 965.2857 - This has a remainder. 7 is not a factor.
6,757 ÷ 11 = 614.2727 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,757 ÷ 29 = 233 - No remainder! 29 is one of the factors!
233 ÷ 29 = 8.0345 - There is a remainder. We can't divide by 29 evenly anymore. Let's try the next prime number
233 ÷ 31 = 7.5161 - This has a remainder. 31 is not a factor.
233 ÷ 37 = 6.2973 - This has a remainder. 37 is not a factor.
233 ÷ 41 = 5.6829 - This has a remainder. 41 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
233 ÷ 233 = 1 - No remainder! 233 is one of the factors!

The orange divisor(s) above are the prime factors of the number 52,542,432. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 29 x 233 = 52,542,432. It can also be written in exponential form as 25 x 35 x 291 x 2331.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 52,542,432.

52,542,432
Factor Arrows
226,271,216
Factor Arrows
213,135,608
Factor Arrows
26,567,804
Factor Arrows
23,283,902
Factor Arrows
21,641,951
Factor Arrows
3547,317
Factor Arrows
3182,439
Factor Arrows
360,813
Factor Arrows
320,271
Factor Arrows
36,757
Factor Arrows
29233

More Prime Factorization Examples

52,542,43052,542,43152,542,43352,542,434
21 x 51 x 4871 x 10,7891431 x 1,221,91713171 x 165,749121 x 71 x 3,753,0311

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