Q: What is the prime factorization of the number 6,020,096?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5,879
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5,879 }
  • Written in exponential form: 210 x 5,8791

Why is the prime factorization of 6,020,096 written as 210 x 5,8791?

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 6,020,096

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 6,020,096 by 2

6,020,096 ÷ 2 = 3,010,048 - No remainder! 2 is one of the factors!
3,010,048 ÷ 2 = 1,505,024 - No remainder! 2 is one of the factors!
1,505,024 ÷ 2 = 752,512 - No remainder! 2 is one of the factors!
752,512 ÷ 2 = 376,256 - No remainder! 2 is one of the factors!
376,256 ÷ 2 = 188,128 - No remainder! 2 is one of the factors!
188,128 ÷ 2 = 94,064 - No remainder! 2 is one of the factors!
94,064 ÷ 2 = 47,032 - No remainder! 2 is one of the factors!
47,032 ÷ 2 = 23,516 - No remainder! 2 is one of the factors!
23,516 ÷ 2 = 11,758 - No remainder! 2 is one of the factors!
11,758 ÷ 2 = 5,879 - No remainder! 2 is one of the factors!
5,879 ÷ 2 = 2,939.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
5,879 ÷ 3 = 1,959.6667 - This has a remainder. 3 is not a factor.
5,879 ÷ 5 = 1,175.8 - This has a remainder. 5 is not a factor.
5,879 ÷ 7 = 839.8571 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
5,879 ÷ 5,879 = 1 - No remainder! 5,879 is one of the factors!

The orange divisor(s) above are the prime factors of the number 6,020,096. 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 2 x 5,879 = 6,020,096. It can also be written in exponential form as 210 x 5,8791.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 6,020,096.

6,020,096
Factor Arrows
23,010,048
Factor Arrows
21,505,024
Factor Arrows
2752,512
Factor Arrows
2376,256
Factor Arrows
2188,128
Factor Arrows
294,064
Factor Arrows
247,032
Factor Arrows
223,516
Factor Arrows
211,758
Factor Arrows
25,879

More Prime Factorization Examples

6,020,0946,020,0956,020,0976,020,098
21 x 31 x 1,003,349151 x 1,204,019131 x 4671 x 4,297121 x 71 x 430,0071

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