Q: What is the prime factorization of the number 387,392?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 6,053
    • or also written as { 2, 2, 2, 2, 2, 2, 6,053 }
  • Written in exponential form: 26 x 6,0531

Why is the prime factorization of 387,392 written as 26 x 6,0531?

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 387,392

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 387,392 by 2

387,392 ÷ 2 = 193,696 - No remainder! 2 is one of the factors!
193,696 ÷ 2 = 96,848 - No remainder! 2 is one of the factors!
96,848 ÷ 2 = 48,424 - No remainder! 2 is one of the factors!
48,424 ÷ 2 = 24,212 - No remainder! 2 is one of the factors!
24,212 ÷ 2 = 12,106 - No remainder! 2 is one of the factors!
12,106 ÷ 2 = 6,053 - No remainder! 2 is one of the factors!
6,053 ÷ 2 = 3,026.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
6,053 ÷ 3 = 2,017.6667 - This has a remainder. 3 is not a factor.
6,053 ÷ 5 = 1,210.6 - This has a remainder. 5 is not a factor.
6,053 ÷ 7 = 864.7143 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,053 ÷ 6,053 = 1 - No remainder! 6,053 is one of the factors!

The orange divisor(s) above are the prime factors of the number 387,392. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 6,053 = 387,392. It can also be written in exponential form as 26 x 6,0531.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 387,392.

387,392
Factor Arrows
2193,696
Factor Arrows
296,848
Factor Arrows
248,424
Factor Arrows
224,212
Factor Arrows
212,106
Factor Arrows
26,053

More Prime Factorization Examples

387,390387,391387,393387,394
21 x 31 x 51 x 371 x 3491191 x 20,389131 x 1391 x 929121 x 72 x 591 x 671

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