Q: What is the prime factorization of the number 111,002,112?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 17 x 109
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 13, 17, 109 }
  • Written in exponential form: 29 x 32 x 131 x 171 x 1091

Why is the prime factorization of 111,002,112 written as 29 x 32 x 131 x 171 x 1091?

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 111,002,112

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 111,002,112 by 2

111,002,112 ÷ 2 = 55,501,056 - No remainder! 2 is one of the factors!
55,501,056 ÷ 2 = 27,750,528 - No remainder! 2 is one of the factors!
27,750,528 ÷ 2 = 13,875,264 - No remainder! 2 is one of the factors!
13,875,264 ÷ 2 = 6,937,632 - No remainder! 2 is one of the factors!
6,937,632 ÷ 2 = 3,468,816 - No remainder! 2 is one of the factors!
3,468,816 ÷ 2 = 1,734,408 - No remainder! 2 is one of the factors!
1,734,408 ÷ 2 = 867,204 - No remainder! 2 is one of the factors!
867,204 ÷ 2 = 433,602 - No remainder! 2 is one of the factors!
433,602 ÷ 2 = 216,801 - No remainder! 2 is one of the factors!
216,801 ÷ 2 = 108,400.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
216,801 ÷ 3 = 72,267 - No remainder! 3 is one of the factors!
72,267 ÷ 3 = 24,089 - No remainder! 3 is one of the factors!
24,089 ÷ 3 = 8,029.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
24,089 ÷ 5 = 4,817.8 - This has a remainder. 5 is not a factor.
24,089 ÷ 7 = 3,441.2857 - This has a remainder. 7 is not a factor.
24,089 ÷ 11 = 2,189.9091 - This has a remainder. 11 is not a factor.
24,089 ÷ 13 = 1,853 - No remainder! 13 is one of the factors!
1,853 ÷ 13 = 142.5385 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
1,853 ÷ 17 = 109 - No remainder! 17 is one of the factors!
109 ÷ 17 = 6.4118 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
109 ÷ 19 = 5.7368 - This has a remainder. 19 is not a factor.
109 ÷ 23 = 4.7391 - This has a remainder. 23 is not a factor.
109 ÷ 29 = 3.7586 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
109 ÷ 109 = 1 - No remainder! 109 is one of the factors!

The orange divisor(s) above are the prime factors of the number 111,002,112. 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 3 x 3 x 13 x 17 x 109 = 111,002,112. It can also be written in exponential form as 29 x 32 x 131 x 171 x 1091.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 111,002,112.

111,002,112
Factor Arrows
255,501,056
Factor Arrows
227,750,528
Factor Arrows
213,875,264
Factor Arrows
26,937,632
Factor Arrows
23,468,816
Factor Arrows
21,734,408
Factor Arrows
2867,204
Factor Arrows
2433,602
Factor Arrows
2216,801
Factor Arrows
372,267
Factor Arrows
324,089
Factor Arrows
131,853
Factor Arrows
17109

More Prime Factorization Examples

111,002,110111,002,111111,002,113111,002,114
21 x 51 x 711 x 791 x 1,9791111 x 291 x 347,96913,6171 x 30,689121 x 5,6931 x 9,7491

Try the factor calculator

Explore more about the number 111,002,112:


Ask a Question