Q: What is the prime factorization of the number 118,725,888?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 154,591
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 3, 154,591 }
  • Written in exponential form: 28 x 31 x 154,5911

Why is the prime factorization of 118,725,888 written as 28 x 31 x 154,5911?

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 118,725,888

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 118,725,888 by 2

118,725,888 ÷ 2 = 59,362,944 - No remainder! 2 is one of the factors!
59,362,944 ÷ 2 = 29,681,472 - No remainder! 2 is one of the factors!
29,681,472 ÷ 2 = 14,840,736 - No remainder! 2 is one of the factors!
14,840,736 ÷ 2 = 7,420,368 - No remainder! 2 is one of the factors!
7,420,368 ÷ 2 = 3,710,184 - No remainder! 2 is one of the factors!
3,710,184 ÷ 2 = 1,855,092 - No remainder! 2 is one of the factors!
1,855,092 ÷ 2 = 927,546 - No remainder! 2 is one of the factors!
927,546 ÷ 2 = 463,773 - No remainder! 2 is one of the factors!
463,773 ÷ 2 = 231,886.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
463,773 ÷ 3 = 154,591 - No remainder! 3 is one of the factors!
154,591 ÷ 3 = 51,530.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
154,591 ÷ 5 = 30,918.2 - This has a remainder. 5 is not a factor.
154,591 ÷ 7 = 22,084.4286 - This has a remainder. 7 is not a factor.
154,591 ÷ 11 = 14,053.7273 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
154,591 ÷ 154,591 = 1 - No remainder! 154,591 is one of the factors!

The orange divisor(s) above are the prime factors of the number 118,725,888. 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 3 x 154,591 = 118,725,888. It can also be written in exponential form as 28 x 31 x 154,5911.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 118,725,888.

118,725,888
Factor Arrows
259,362,944
Factor Arrows
229,681,472
Factor Arrows
214,840,736
Factor Arrows
27,420,368
Factor Arrows
23,710,184
Factor Arrows
21,855,092
Factor Arrows
2927,546
Factor Arrows
2463,773
Factor Arrows
3154,591

More Prime Factorization Examples

118,725,886118,725,887118,725,889118,725,890
21 x 611 x 731 x 13,331171 x 16,960,8411191 x 6,248,731121 x 51 x 6831 x 17,3831

Try the factor calculator

Explore more about the number 118,725,888:


Ask a Question