Q: What is the prime factorization of the number 15,560,328?

 A:
  • The prime factors are: 2 x 2 x 2 x 3 x 7 x 23 x 4,027
    • or also written as { 2, 2, 2, 3, 7, 23, 4,027 }
  • Written in exponential form: 23 x 31 x 71 x 231 x 4,0271

Why is the prime factorization of 15,560,328 written as 23 x 31 x 71 x 231 x 4,0271?

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 15,560,328

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 15,560,328 by 2

15,560,328 ÷ 2 = 7,780,164 - No remainder! 2 is one of the factors!
7,780,164 ÷ 2 = 3,890,082 - No remainder! 2 is one of the factors!
3,890,082 ÷ 2 = 1,945,041 - No remainder! 2 is one of the factors!
1,945,041 ÷ 2 = 972,520.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,945,041 ÷ 3 = 648,347 - No remainder! 3 is one of the factors!
648,347 ÷ 3 = 216,115.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
648,347 ÷ 5 = 129,669.4 - This has a remainder. 5 is not a factor.
648,347 ÷ 7 = 92,621 - No remainder! 7 is one of the factors!
92,621 ÷ 7 = 13,231.5714 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
92,621 ÷ 11 = 8,420.0909 - This has a remainder. 11 is not a factor.
92,621 ÷ 13 = 7,124.6923 - This has a remainder. 13 is not a factor.
92,621 ÷ 17 = 5,448.2941 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
92,621 ÷ 23 = 4,027 - No remainder! 23 is one of the factors!
4,027 ÷ 23 = 175.087 - There is a remainder. We can't divide by 23 evenly anymore. Let's try the next prime number
4,027 ÷ 29 = 138.8621 - This has a remainder. 29 is not a factor.
4,027 ÷ 31 = 129.9032 - This has a remainder. 31 is not a factor.
4,027 ÷ 37 = 108.8378 - This has a remainder. 37 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
4,027 ÷ 4,027 = 1 - No remainder! 4,027 is one of the factors!

The orange divisor(s) above are the prime factors of the number 15,560,328. If we put all of it together we have the factors 2 x 2 x 2 x 3 x 7 x 23 x 4,027 = 15,560,328. It can also be written in exponential form as 23 x 31 x 71 x 231 x 4,0271.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 15,560,328.

15,560,328
Factor Arrows
27,780,164
Factor Arrows
23,890,082
Factor Arrows
21,945,041
Factor Arrows
3648,347
Factor Arrows
792,621
Factor Arrows
234,027

More Prime Factorization Examples

15,560,32615,560,32715,560,32915,560,330
21 x 311 x 1131 x 2,2211291 x 536,563115,560,329121 x 51 x 8291 x 1,8771

Try the factor calculator

Explore more about the number 15,560,328:


Ask a Question