Q: What is the prime factorization of the number 38,430,096?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 101 x 7,927
    • or also written as { 2, 2, 2, 2, 3, 101, 7,927 }
  • Written in exponential form: 24 x 31 x 1011 x 7,9271

Why is the prime factorization of 38,430,096 written as 24 x 31 x 1011 x 7,9271?

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 38,430,096

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 38,430,096 by 2

38,430,096 ÷ 2 = 19,215,048 - No remainder! 2 is one of the factors!
19,215,048 ÷ 2 = 9,607,524 - No remainder! 2 is one of the factors!
9,607,524 ÷ 2 = 4,803,762 - No remainder! 2 is one of the factors!
4,803,762 ÷ 2 = 2,401,881 - No remainder! 2 is one of the factors!
2,401,881 ÷ 2 = 1,200,940.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,401,881 ÷ 3 = 800,627 - No remainder! 3 is one of the factors!
800,627 ÷ 3 = 266,875.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
800,627 ÷ 5 = 160,125.4 - This has a remainder. 5 is not a factor.
800,627 ÷ 7 = 114,375.2857 - This has a remainder. 7 is not a factor.
800,627 ÷ 11 = 72,784.2727 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
800,627 ÷ 101 = 7,927 - No remainder! 101 is one of the factors!
7,927 ÷ 101 = 78.4851 - There is a remainder. We can't divide by 101 evenly anymore. Let's try the next prime number
7,927 ÷ 103 = 76.9612 - This has a remainder. 103 is not a factor.
7,927 ÷ 107 = 74.0841 - This has a remainder. 107 is not a factor.
7,927 ÷ 109 = 72.7248 - This has a remainder. 109 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
7,927 ÷ 7,927 = 1 - No remainder! 7,927 is one of the factors!

The orange divisor(s) above are the prime factors of the number 38,430,096. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 101 x 7,927 = 38,430,096. It can also be written in exponential form as 24 x 31 x 1011 x 7,9271.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 38,430,096.

38,430,096
Factor Arrows
219,215,048
Factor Arrows
29,607,524
Factor Arrows
24,803,762
Factor Arrows
22,401,881
Factor Arrows
3800,627
Factor Arrows
1017,927

More Prime Factorization Examples

38,430,09438,430,09538,430,09738,430,098
21 x 1,9731 x 9,739151 x 111 x 698,72911,4291 x 26,893121 x 71 x 171 x 161,4711

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