Q: What is the prime factorization of the number 13,104?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 7 x 13
    • or also written as { 2, 2, 2, 2, 3, 3, 7, 13 }
  • Written in exponential form: 24 x 32 x 71 x 131

Why is the prime factorization of 13,104 written as 24 x 32 x 71 x 131?

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 13,104

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 13,104 by 2

13,104 ÷ 2 = 6,552 - No remainder! 2 is one of the factors!
6,552 ÷ 2 = 3,276 - No remainder! 2 is one of the factors!
3,276 ÷ 2 = 1,638 - No remainder! 2 is one of the factors!
1,638 ÷ 2 = 819 - No remainder! 2 is one of the factors!
819 ÷ 2 = 409.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
819 ÷ 3 = 273 - No remainder! 3 is one of the factors!
273 ÷ 3 = 91 - No remainder! 3 is one of the factors!
91 ÷ 3 = 30.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
91 ÷ 5 = 18.2 - This has a remainder. 5 is not a factor.
91 ÷ 7 = 13 - No remainder! 7 is one of the factors!
13 ÷ 7 = 1.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
13 ÷ 11 = 1.1818 - This has a remainder. 11 is not a factor.
13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 13,104. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 7 x 13 = 13,104. It can also be written in exponential form as 24 x 32 x 71 x 131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 13,104.

13,104
Factor Arrows
26,552
Factor Arrows
23,276
Factor Arrows
21,638
Factor Arrows
2819
Factor Arrows
3273
Factor Arrows
391
Factor Arrows
713

More Prime Factorization Examples

13,10213,10313,10513,106
21 x 6,551113,103151 x 2,621121 x 6,5531

Try the factor calculator

Explore more about the number 13,104:


Ask a Question