Q: What is the prime factorization of the number 188,928?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 41
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 41 }
  • Written in exponential form: 29 x 32 x 411

Why is the prime factorization of 188,928 written as 29 x 32 x 411?

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 188,928

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 188,928 by 2

188,928 ÷ 2 = 94,464 - No remainder! 2 is one of the factors!
94,464 ÷ 2 = 47,232 - No remainder! 2 is one of the factors!
47,232 ÷ 2 = 23,616 - No remainder! 2 is one of the factors!
23,616 ÷ 2 = 11,808 - No remainder! 2 is one of the factors!
11,808 ÷ 2 = 5,904 - No remainder! 2 is one of the factors!
5,904 ÷ 2 = 2,952 - No remainder! 2 is one of the factors!
2,952 ÷ 2 = 1,476 - No remainder! 2 is one of the factors!
1,476 ÷ 2 = 738 - No remainder! 2 is one of the factors!
738 ÷ 2 = 369 - No remainder! 2 is one of the factors!
369 ÷ 2 = 184.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
369 ÷ 3 = 123 - No remainder! 3 is one of the factors!
123 ÷ 3 = 41 - No remainder! 3 is one of the factors!
41 ÷ 3 = 13.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
41 ÷ 5 = 8.2 - This has a remainder. 5 is not a factor.
41 ÷ 7 = 5.8571 - This has a remainder. 7 is not a factor.
41 ÷ 11 = 3.7273 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
41 ÷ 41 = 1 - No remainder! 41 is one of the factors!

The orange divisor(s) above are the prime factors of the number 188,928. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 41 = 188,928. It can also be written in exponential form as 29 x 32 x 411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 188,928.

188,928
Factor Arrows
294,464
Factor Arrows
247,232
Factor Arrows
223,616
Factor Arrows
211,808
Factor Arrows
25,904
Factor Arrows
22,952
Factor Arrows
21,476
Factor Arrows
2738
Factor Arrows
2369
Factor Arrows
3123
Factor Arrows
341

More Prime Factorization Examples

188,926188,927188,929188,930
21 x 94,4631188,9271131 x 14,533121 x 51 x 71 x 2,6991

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