Q: What is the prime factorization of the number 472,176?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1,093
    • or also written as { 2, 2, 2, 2, 3, 3, 3, 1,093 }
  • Written in exponential form: 24 x 33 x 1,0931

Why is the prime factorization of 472,176 written as 24 x 33 x 1,0931?

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 472,176

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 472,176 by 2

472,176 ÷ 2 = 236,088 - No remainder! 2 is one of the factors!
236,088 ÷ 2 = 118,044 - No remainder! 2 is one of the factors!
118,044 ÷ 2 = 59,022 - No remainder! 2 is one of the factors!
59,022 ÷ 2 = 29,511 - No remainder! 2 is one of the factors!
29,511 ÷ 2 = 14,755.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
29,511 ÷ 3 = 9,837 - No remainder! 3 is one of the factors!
9,837 ÷ 3 = 3,279 - No remainder! 3 is one of the factors!
3,279 ÷ 3 = 1,093 - No remainder! 3 is one of the factors!
1,093 ÷ 3 = 364.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,093 ÷ 5 = 218.6 - This has a remainder. 5 is not a factor.
1,093 ÷ 7 = 156.1429 - This has a remainder. 7 is not a factor.
1,093 ÷ 11 = 99.3636 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,093 ÷ 1,093 = 1 - No remainder! 1,093 is one of the factors!

The orange divisor(s) above are the prime factors of the number 472,176. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1,093 = 472,176. It can also be written in exponential form as 24 x 33 x 1,0931.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 472,176.

472,176
Factor Arrows
2236,088
Factor Arrows
2118,044
Factor Arrows
259,022
Factor Arrows
229,511
Factor Arrows
39,837
Factor Arrows
33,279
Factor Arrows
31,093

More Prime Factorization Examples

472,174472,175472,177472,178
21 x 236,087152 x 111 x 171 x 1011531 x 591 x 151121 x 71 x 291 x 1,1631

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