Q: What is the prime factorization of the number 22,134,016?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 86,461
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 86,461 }
  • Written in exponential form: 28 x 86,4611

Why is the prime factorization of 22,134,016 written as 28 x 86,4611?

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 22,134,016

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 22,134,016 by 2

22,134,016 ÷ 2 = 11,067,008 - No remainder! 2 is one of the factors!
11,067,008 ÷ 2 = 5,533,504 - No remainder! 2 is one of the factors!
5,533,504 ÷ 2 = 2,766,752 - No remainder! 2 is one of the factors!
2,766,752 ÷ 2 = 1,383,376 - No remainder! 2 is one of the factors!
1,383,376 ÷ 2 = 691,688 - No remainder! 2 is one of the factors!
691,688 ÷ 2 = 345,844 - No remainder! 2 is one of the factors!
345,844 ÷ 2 = 172,922 - No remainder! 2 is one of the factors!
172,922 ÷ 2 = 86,461 - No remainder! 2 is one of the factors!
86,461 ÷ 2 = 43,230.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
86,461 ÷ 3 = 28,820.3333 - This has a remainder. 3 is not a factor.
86,461 ÷ 5 = 17,292.2 - This has a remainder. 5 is not a factor.
86,461 ÷ 7 = 12,351.5714 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
86,461 ÷ 86,461 = 1 - No remainder! 86,461 is one of the factors!

The orange divisor(s) above are the prime factors of the number 22,134,016. 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 86,461 = 22,134,016. It can also be written in exponential form as 28 x 86,4611.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 22,134,016.

22,134,016
Factor Arrows
211,067,008
Factor Arrows
25,533,504
Factor Arrows
22,766,752
Factor Arrows
21,383,376
Factor Arrows
2691,688
Factor Arrows
2345,844
Factor Arrows
2172,922
Factor Arrows
286,461

More Prime Factorization Examples

22,134,01422,134,01522,134,01722,134,018
21 x 71 x 411 x 38,561132 x 51 x 491,8671171 x 1571 x 8,293121 x 31 x 291 x 127,2071

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