Q: What is the prime factorization of the number 15,420,896?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 223 x 2,161
    • or also written as { 2, 2, 2, 2, 2, 223, 2,161 }
  • Written in exponential form: 25 x 2231 x 2,1611

Why is the prime factorization of 15,420,896 written as 25 x 2231 x 2,1611?

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 15,420,896

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 15,420,896 by 2

15,420,896 ÷ 2 = 7,710,448 - No remainder! 2 is one of the factors!
7,710,448 ÷ 2 = 3,855,224 - No remainder! 2 is one of the factors!
3,855,224 ÷ 2 = 1,927,612 - No remainder! 2 is one of the factors!
1,927,612 ÷ 2 = 963,806 - No remainder! 2 is one of the factors!
963,806 ÷ 2 = 481,903 - No remainder! 2 is one of the factors!
481,903 ÷ 2 = 240,951.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
481,903 ÷ 3 = 160,634.3333 - This has a remainder. 3 is not a factor.
481,903 ÷ 5 = 96,380.6 - This has a remainder. 5 is not a factor.
481,903 ÷ 7 = 68,843.2857 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
481,903 ÷ 223 = 2,161 - No remainder! 223 is one of the factors!
2,161 ÷ 223 = 9.6906 - There is a remainder. We can't divide by 223 evenly anymore. Let's try the next prime number
2,161 ÷ 227 = 9.5198 - This has a remainder. 227 is not a factor.
2,161 ÷ 229 = 9.4367 - This has a remainder. 229 is not a factor.
2,161 ÷ 233 = 9.2747 - This has a remainder. 233 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,161 ÷ 2,161 = 1 - No remainder! 2,161 is one of the factors!

The orange divisor(s) above are the prime factors of the number 15,420,896. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 223 x 2,161 = 15,420,896. It can also be written in exponential form as 25 x 2231 x 2,1611.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 15,420,896.

15,420,896
Factor Arrows
27,710,448
Factor Arrows
23,855,224
Factor Arrows
21,927,612
Factor Arrows
2963,806
Factor Arrows
2481,903
Factor Arrows
2232,161

More Prime Factorization Examples

15,420,89415,420,89515,420,89715,420,898
21 x 31 x 191 x 135,271151 x 71 x 291 x 15,193132 x 371 x 46,309121 x 7,710,4491

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