Q: What is the prime factorization of the number 124,333,056?

 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 3 x 3 x 3 x 3 x 1,499
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 1,499 }
  • Written in exponential form: 210 x 34 x 1,4991

Why is the prime factorization of 124,333,056 written as 210 x 34 x 1,4991?

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 124,333,056

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 124,333,056 by 2

124,333,056 ÷ 2 = 62,166,528 - No remainder! 2 is one of the factors!
62,166,528 ÷ 2 = 31,083,264 - No remainder! 2 is one of the factors!
31,083,264 ÷ 2 = 15,541,632 - No remainder! 2 is one of the factors!
15,541,632 ÷ 2 = 7,770,816 - No remainder! 2 is one of the factors!
7,770,816 ÷ 2 = 3,885,408 - No remainder! 2 is one of the factors!
3,885,408 ÷ 2 = 1,942,704 - No remainder! 2 is one of the factors!
1,942,704 ÷ 2 = 971,352 - No remainder! 2 is one of the factors!
971,352 ÷ 2 = 485,676 - No remainder! 2 is one of the factors!
485,676 ÷ 2 = 242,838 - No remainder! 2 is one of the factors!
242,838 ÷ 2 = 121,419 - No remainder! 2 is one of the factors!
121,419 ÷ 2 = 60,709.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
121,419 ÷ 3 = 40,473 - No remainder! 3 is one of the factors!
40,473 ÷ 3 = 13,491 - No remainder! 3 is one of the factors!
13,491 ÷ 3 = 4,497 - No remainder! 3 is one of the factors!
4,497 ÷ 3 = 1,499 - No remainder! 3 is one of the factors!
1,499 ÷ 3 = 499.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,499 ÷ 5 = 299.8 - This has a remainder. 5 is not a factor.
1,499 ÷ 7 = 214.1429 - This has a remainder. 7 is not a factor.
1,499 ÷ 11 = 136.2727 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,499 ÷ 1,499 = 1 - No remainder! 1,499 is one of the factors!

The orange divisor(s) above are the prime factors of the number 124,333,056. 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 3 x 3 x 3 x 3 x 1,499 = 124,333,056. It can also be written in exponential form as 210 x 34 x 1,4991.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 124,333,056.

124,333,056
Factor Arrows
262,166,528
Factor Arrows
231,083,264
Factor Arrows
215,541,632
Factor Arrows
27,770,816
Factor Arrows
23,885,408
Factor Arrows
21,942,704
Factor Arrows
2971,352
Factor Arrows
2485,676
Factor Arrows
2242,838
Factor Arrows
2121,419
Factor Arrows
340,473
Factor Arrows
313,491
Factor Arrows
34,497
Factor Arrows
31,499

More Prime Factorization Examples

124,333,054124,333,055124,333,057124,333,058
21 x 62,166,527151 x 71 x 111 x 191 x 231 x 73915871 x 211,811121 x 2391 x 260,1111

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