Q: What is the prime factorization of the number 15,563,120?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 5 x 227 x 857
    • or also written as { 2, 2, 2, 2, 5, 227, 857 }
  • Written in exponential form: 24 x 51 x 2271 x 8571

Why is the prime factorization of 15,563,120 written as 24 x 51 x 2271 x 8571?

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 15,563,120

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 15,563,120 by 2

15,563,120 ÷ 2 = 7,781,560 - No remainder! 2 is one of the factors!
7,781,560 ÷ 2 = 3,890,780 - No remainder! 2 is one of the factors!
3,890,780 ÷ 2 = 1,945,390 - No remainder! 2 is one of the factors!
1,945,390 ÷ 2 = 972,695 - No remainder! 2 is one of the factors!
972,695 ÷ 2 = 486,347.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
972,695 ÷ 3 = 324,231.6667 - This has a remainder. 3 is not a factor.
972,695 ÷ 5 = 194,539 - No remainder! 5 is one of the factors!
194,539 ÷ 5 = 38,907.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
194,539 ÷ 7 = 27,791.2857 - This has a remainder. 7 is not a factor.
194,539 ÷ 11 = 17,685.3636 - This has a remainder. 11 is not a factor.
194,539 ÷ 13 = 14,964.5385 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
194,539 ÷ 227 = 857 - No remainder! 227 is one of the factors!
857 ÷ 227 = 3.7753 - There is a remainder. We can't divide by 227 evenly anymore. Let's try the next prime number
857 ÷ 229 = 3.7424 - This has a remainder. 229 is not a factor.
857 ÷ 233 = 3.6781 - This has a remainder. 233 is not a factor.
857 ÷ 239 = 3.5858 - This has a remainder. 239 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
857 ÷ 857 = 1 - No remainder! 857 is one of the factors!

The orange divisor(s) above are the prime factors of the number 15,563,120. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 5 x 227 x 857 = 15,563,120. It can also be written in exponential form as 24 x 51 x 2271 x 8571.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 15,563,120.

15,563,120
Factor Arrows
27,781,560
Factor Arrows
23,890,780
Factor Arrows
21,945,390
Factor Arrows
2972,695
Factor Arrows
5194,539
Factor Arrows
227857

More Prime Factorization Examples

15,563,11815,563,11915,563,12115,563,122
21 x 31 x 2,593,8531111 x 131 x 431 x 2,531131 x 71 x 741,101121 x 7,781,5611

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