Q: What is the prime factorization of the number 124,250,112?

 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 2 x 3 x 3 x 3 x 3 x 7 x 107
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 107 }
  • Written in exponential form: 211 x 34 x 71 x 1071

Why is the prime factorization of 124,250,112 written as 211 x 34 x 71 x 1071?

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 124,250,112

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 124,250,112 by 2

124,250,112 ÷ 2 = 62,125,056 - No remainder! 2 is one of the factors!
62,125,056 ÷ 2 = 31,062,528 - No remainder! 2 is one of the factors!
31,062,528 ÷ 2 = 15,531,264 - No remainder! 2 is one of the factors!
15,531,264 ÷ 2 = 7,765,632 - No remainder! 2 is one of the factors!
7,765,632 ÷ 2 = 3,882,816 - No remainder! 2 is one of the factors!
3,882,816 ÷ 2 = 1,941,408 - No remainder! 2 is one of the factors!
1,941,408 ÷ 2 = 970,704 - No remainder! 2 is one of the factors!
970,704 ÷ 2 = 485,352 - No remainder! 2 is one of the factors!
485,352 ÷ 2 = 242,676 - No remainder! 2 is one of the factors!
242,676 ÷ 2 = 121,338 - No remainder! 2 is one of the factors!
121,338 ÷ 2 = 60,669 - No remainder! 2 is one of the factors!
60,669 ÷ 2 = 30,334.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
60,669 ÷ 3 = 20,223 - No remainder! 3 is one of the factors!
20,223 ÷ 3 = 6,741 - No remainder! 3 is one of the factors!
6,741 ÷ 3 = 2,247 - No remainder! 3 is one of the factors!
2,247 ÷ 3 = 749 - No remainder! 3 is one of the factors!
749 ÷ 3 = 249.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
749 ÷ 5 = 149.8 - This has a remainder. 5 is not a factor.
749 ÷ 7 = 107 - No remainder! 7 is one of the factors!
107 ÷ 7 = 15.2857 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
107 ÷ 11 = 9.7273 - This has a remainder. 11 is not a factor.
107 ÷ 13 = 8.2308 - This has a remainder. 13 is not a factor.
107 ÷ 17 = 6.2941 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
107 ÷ 107 = 1 - No remainder! 107 is one of the factors!

The orange divisor(s) above are the prime factors of the number 124,250,112. 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 2 x 3 x 3 x 3 x 3 x 7 x 107 = 124,250,112. It can also be written in exponential form as 211 x 34 x 71 x 1071.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 124,250,112.

124,250,112
Factor Arrows
262,125,056
Factor Arrows
231,062,528
Factor Arrows
215,531,264
Factor Arrows
27,765,632
Factor Arrows
23,882,816
Factor Arrows
21,941,408
Factor Arrows
2970,704
Factor Arrows
2485,352
Factor Arrows
2242,676
Factor Arrows
2121,338
Factor Arrows
260,669
Factor Arrows
320,223
Factor Arrows
36,741
Factor Arrows
32,247
Factor Arrows
3749
Factor Arrows
7107

More Prime Factorization Examples

124,250,110124,250,111124,250,113124,250,114
21 x 51 x 171 x 4091 x 1,7871124,250,1111131 x 971 x 98,533121 x 1571 x 395,7011

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