Q: What is the prime factorization of the number 6,091,008?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 11 x 103
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 11, 103 }
  • Written in exponential form: 28 x 31 x 71 x 111 x 1031

Why is the prime factorization of 6,091,008 written as 28 x 31 x 71 x 111 x 1031?

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 6,091,008

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 6,091,008 by 2

6,091,008 ÷ 2 = 3,045,504 - No remainder! 2 is one of the factors!
3,045,504 ÷ 2 = 1,522,752 - No remainder! 2 is one of the factors!
1,522,752 ÷ 2 = 761,376 - No remainder! 2 is one of the factors!
761,376 ÷ 2 = 380,688 - No remainder! 2 is one of the factors!
380,688 ÷ 2 = 190,344 - No remainder! 2 is one of the factors!
190,344 ÷ 2 = 95,172 - No remainder! 2 is one of the factors!
95,172 ÷ 2 = 47,586 - No remainder! 2 is one of the factors!
47,586 ÷ 2 = 23,793 - No remainder! 2 is one of the factors!
23,793 ÷ 2 = 11,896.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
23,793 ÷ 3 = 7,931 - No remainder! 3 is one of the factors!
7,931 ÷ 3 = 2,643.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
7,931 ÷ 5 = 1,586.2 - This has a remainder. 5 is not a factor.
7,931 ÷ 7 = 1,133 - No remainder! 7 is one of the factors!
1,133 ÷ 7 = 161.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
1,133 ÷ 11 = 103 - No remainder! 11 is one of the factors!
103 ÷ 11 = 9.3636 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
103 ÷ 13 = 7.9231 - This has a remainder. 13 is not a factor.
103 ÷ 17 = 6.0588 - This has a remainder. 17 is not a factor.
103 ÷ 19 = 5.4211 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
103 ÷ 103 = 1 - No remainder! 103 is one of the factors!

The orange divisor(s) above are the prime factors of the number 6,091,008. 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 3 x 7 x 11 x 103 = 6,091,008. It can also be written in exponential form as 28 x 31 x 71 x 111 x 1031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 6,091,008.

6,091,008
Factor Arrows
23,045,504
Factor Arrows
21,522,752
Factor Arrows
2761,376
Factor Arrows
2380,688
Factor Arrows
2190,344
Factor Arrows
295,172
Factor Arrows
247,586
Factor Arrows
223,793
Factor Arrows
37,931
Factor Arrows
71,133
Factor Arrows
11103

More Prime Factorization Examples

6,091,0066,091,0076,091,0096,091,010
21 x 3,045,5031131 x 1011 x 4,63912831 x 21,523121 x 51 x 609,1011

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