Q: What is the prime factorization of the number 583,200?

 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 3 x 5 x 5
    • or also written as { 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5 }
  • Written in exponential form: 25 x 36 x 52

Why is the prime factorization of 583,200 written as 25 x 36 x 52?

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 583,200

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 583,200 by 2

583,200 ÷ 2 = 291,600 - No remainder! 2 is one of the factors!
291,600 ÷ 2 = 145,800 - No remainder! 2 is one of the factors!
145,800 ÷ 2 = 72,900 - No remainder! 2 is one of the factors!
72,900 ÷ 2 = 36,450 - No remainder! 2 is one of the factors!
36,450 ÷ 2 = 18,225 - No remainder! 2 is one of the factors!
18,225 ÷ 2 = 9,112.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
18,225 ÷ 3 = 6,075 - No remainder! 3 is one of the factors!
6,075 ÷ 3 = 2,025 - No remainder! 3 is one of the factors!
2,025 ÷ 3 = 675 - No remainder! 3 is one of the factors!
675 ÷ 3 = 225 - No remainder! 3 is one of the factors!
225 ÷ 3 = 75 - No remainder! 3 is one of the factors!
75 ÷ 3 = 25 - No remainder! 3 is one of the factors!
25 ÷ 3 = 8.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
25 ÷ 5 = 5 - No remainder! 5 is one of the factors!
5 ÷ 5 = 1 - No remainder! 5 is one of the factors!

The orange divisor(s) above are the prime factors of the number 583,200. 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 3 x 5 x 5 = 583,200. It can also be written in exponential form as 25 x 36 x 52.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 583,200.

583,200
Factor Arrows
2291,600
Factor Arrows
2145,800
Factor Arrows
272,900
Factor Arrows
236,450
Factor Arrows
218,225
Factor Arrows
36,075
Factor Arrows
32,025
Factor Arrows
3675
Factor Arrows
3225
Factor Arrows
375
Factor Arrows
325
Factor Arrows
55

More Prime Factorization Examples

583,198583,199583,201583,202
21 x 72 x 111 x 54112331 x 2,50316431 x 907121 x 172 x 1,0091

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