Q: What is the prime factorization of the number 13,108,736?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 25,603
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 25,603 }
  • Written in exponential form: 29 x 25,6031

Why is the prime factorization of 13,108,736 written as 29 x 25,6031?

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 13,108,736

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 13,108,736 by 2

13,108,736 ÷ 2 = 6,554,368 - No remainder! 2 is one of the factors!
6,554,368 ÷ 2 = 3,277,184 - No remainder! 2 is one of the factors!
3,277,184 ÷ 2 = 1,638,592 - No remainder! 2 is one of the factors!
1,638,592 ÷ 2 = 819,296 - No remainder! 2 is one of the factors!
819,296 ÷ 2 = 409,648 - No remainder! 2 is one of the factors!
409,648 ÷ 2 = 204,824 - No remainder! 2 is one of the factors!
204,824 ÷ 2 = 102,412 - No remainder! 2 is one of the factors!
102,412 ÷ 2 = 51,206 - No remainder! 2 is one of the factors!
51,206 ÷ 2 = 25,603 - No remainder! 2 is one of the factors!
25,603 ÷ 2 = 12,801.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
25,603 ÷ 3 = 8,534.3333 - This has a remainder. 3 is not a factor.
25,603 ÷ 5 = 5,120.6 - This has a remainder. 5 is not a factor.
25,603 ÷ 7 = 3,657.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
25,603 ÷ 25,603 = 1 - No remainder! 25,603 is one of the factors!

The orange divisor(s) above are the prime factors of the number 13,108,736. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 25,603 = 13,108,736. It can also be written in exponential form as 29 x 25,6031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 13,108,736.

13,108,736
Factor Arrows
26,554,368
Factor Arrows
23,277,184
Factor Arrows
21,638,592
Factor Arrows
2819,296
Factor Arrows
2409,648
Factor Arrows
2204,824
Factor Arrows
2102,412
Factor Arrows
251,206
Factor Arrows
225,603

More Prime Factorization Examples

13,108,73413,108,73513,108,73713,108,738
21 x 32 x 171 x 42,839151 x 231 x 113,989131 x 4,369,579121 x 591 x 111,0911

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