Q: What is the prime factorization of the number 30,421,504?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 59,417
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 59,417 }
  • Written in exponential form: 29 x 59,4171

Why is the prime factorization of 30,421,504 written as 29 x 59,4171?

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 30,421,504

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 30,421,504 by 2

30,421,504 ÷ 2 = 15,210,752 - No remainder! 2 is one of the factors!
15,210,752 ÷ 2 = 7,605,376 - No remainder! 2 is one of the factors!
7,605,376 ÷ 2 = 3,802,688 - No remainder! 2 is one of the factors!
3,802,688 ÷ 2 = 1,901,344 - No remainder! 2 is one of the factors!
1,901,344 ÷ 2 = 950,672 - No remainder! 2 is one of the factors!
950,672 ÷ 2 = 475,336 - No remainder! 2 is one of the factors!
475,336 ÷ 2 = 237,668 - No remainder! 2 is one of the factors!
237,668 ÷ 2 = 118,834 - No remainder! 2 is one of the factors!
118,834 ÷ 2 = 59,417 - No remainder! 2 is one of the factors!
59,417 ÷ 2 = 29,708.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
59,417 ÷ 3 = 19,805.6667 - This has a remainder. 3 is not a factor.
59,417 ÷ 5 = 11,883.4 - This has a remainder. 5 is not a factor.
59,417 ÷ 7 = 8,488.1429 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
59,417 ÷ 59,417 = 1 - No remainder! 59,417 is one of the factors!

The orange divisor(s) above are the prime factors of the number 30,421,504. 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 59,417 = 30,421,504. It can also be written in exponential form as 29 x 59,4171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 30,421,504.

30,421,504
Factor Arrows
215,210,752
Factor Arrows
27,605,376
Factor Arrows
23,802,688
Factor Arrows
21,901,344
Factor Arrows
2950,672
Factor Arrows
2475,336
Factor Arrows
2237,668
Factor Arrows
2118,834
Factor Arrows
259,417

More Prime Factorization Examples

30,421,50230,421,50330,421,50530,421,506
21 x 231 x 471 x 14,071132 x 72 x 1011 x 683151 x 1632 x 229121 x 31 x 5,070,2511

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