Q: What is the prime factorization of the number 1,131,008?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 47 x 47
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 47, 47 }
  • Written in exponential form: 29 x 472

Why is the prime factorization of 1,131,008 written as 29 x 472?

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 1,131,008

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 1,131,008 by 2

1,131,008 ÷ 2 = 565,504 - No remainder! 2 is one of the factors!
565,504 ÷ 2 = 282,752 - No remainder! 2 is one of the factors!
282,752 ÷ 2 = 141,376 - No remainder! 2 is one of the factors!
141,376 ÷ 2 = 70,688 - No remainder! 2 is one of the factors!
70,688 ÷ 2 = 35,344 - No remainder! 2 is one of the factors!
35,344 ÷ 2 = 17,672 - No remainder! 2 is one of the factors!
17,672 ÷ 2 = 8,836 - No remainder! 2 is one of the factors!
8,836 ÷ 2 = 4,418 - No remainder! 2 is one of the factors!
4,418 ÷ 2 = 2,209 - No remainder! 2 is one of the factors!
2,209 ÷ 2 = 1,104.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,209 ÷ 3 = 736.3333 - This has a remainder. 3 is not a factor.
2,209 ÷ 5 = 441.8 - This has a remainder. 5 is not a factor.
2,209 ÷ 7 = 315.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,209 ÷ 47 = 47 - No remainder! 47 is one of the factors!
47 ÷ 47 = 1 - No remainder! 47 is one of the factors!

The orange divisor(s) above are the prime factors of the number 1,131,008. 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 47 x 47 = 1,131,008. It can also be written in exponential form as 29 x 472.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,131,008.

1,131,008
Factor Arrows
2565,504
Factor Arrows
2282,752
Factor Arrows
2141,376
Factor Arrows
270,688
Factor Arrows
235,344
Factor Arrows
217,672
Factor Arrows
28,836
Factor Arrows
24,418
Factor Arrows
22,209
Factor Arrows
4747

More Prime Factorization Examples

1,131,0061,131,0071,131,0091,131,010
21 x 31 x 2511 x 75111,0311 x 1,097131 x 111 x 34,273121 x 51 x 171 x 6,6531

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