Q: What is the prime factorization of the number 323,200?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 101
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 5, 5, 101 }
  • Written in exponential form: 27 x 52 x 1011

Why is the prime factorization of 323,200 written as 27 x 52 x 1011?

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 323,200

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 323,200 by 2

323,200 ÷ 2 = 161,600 - No remainder! 2 is one of the factors!
161,600 ÷ 2 = 80,800 - No remainder! 2 is one of the factors!
80,800 ÷ 2 = 40,400 - No remainder! 2 is one of the factors!
40,400 ÷ 2 = 20,200 - No remainder! 2 is one of the factors!
20,200 ÷ 2 = 10,100 - No remainder! 2 is one of the factors!
10,100 ÷ 2 = 5,050 - No remainder! 2 is one of the factors!
5,050 ÷ 2 = 2,525 - No remainder! 2 is one of the factors!
2,525 ÷ 2 = 1,262.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,525 ÷ 3 = 841.6667 - This has a remainder. 3 is not a factor.
2,525 ÷ 5 = 505 - No remainder! 5 is one of the factors!
505 ÷ 5 = 101 - No remainder! 5 is one of the factors!
101 ÷ 5 = 20.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
101 ÷ 7 = 14.4286 - This has a remainder. 7 is not a factor.
101 ÷ 11 = 9.1818 - This has a remainder. 11 is not a factor.
101 ÷ 13 = 7.7692 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
101 ÷ 101 = 1 - No remainder! 101 is one of the factors!

The orange divisor(s) above are the prime factors of the number 323,200. 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 5 x 5 x 101 = 323,200. It can also be written in exponential form as 27 x 52 x 1011.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 323,200.

323,200
Factor Arrows
2161,600
Factor Arrows
280,800
Factor Arrows
240,400
Factor Arrows
220,200
Factor Arrows
210,100
Factor Arrows
25,050
Factor Arrows
22,525
Factor Arrows
5505
Factor Arrows
5101

More Prime Factorization Examples

323,198323,199323,201323,202
21 x 161,599132 x 35,9111323,201121 x 31 x 111 x 591 x 831

Try the factor calculator

Explore more about the number 323,200:


Ask a Question