Q: What is the prime factorization of the number 339,024,440?

 A:
  • The prime factors are: 2 x 2 x 2 x 5 x 293 x 28,927
    • or also written as { 2, 2, 2, 5, 293, 28,927 }
  • Written in exponential form: 23 x 51 x 2931 x 28,9271

Why is the prime factorization of 339,024,440 written as 23 x 51 x 2931 x 28,9271?

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 339,024,440

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 339,024,440 by 2

339,024,440 ÷ 2 = 169,512,220 - No remainder! 2 is one of the factors!
169,512,220 ÷ 2 = 84,756,110 - No remainder! 2 is one of the factors!
84,756,110 ÷ 2 = 42,378,055 - No remainder! 2 is one of the factors!
42,378,055 ÷ 2 = 21,189,027.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
42,378,055 ÷ 3 = 14,126,018.3333 - This has a remainder. 3 is not a factor.
42,378,055 ÷ 5 = 8,475,611 - No remainder! 5 is one of the factors!
8,475,611 ÷ 5 = 1,695,122.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
8,475,611 ÷ 7 = 1,210,801.5714 - This has a remainder. 7 is not a factor.
8,475,611 ÷ 11 = 770,510.0909 - This has a remainder. 11 is not a factor.
8,475,611 ÷ 13 = 651,970.0769 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
8,475,611 ÷ 293 = 28,927 - No remainder! 293 is one of the factors!
28,927 ÷ 293 = 98.727 - There is a remainder. We can't divide by 293 evenly anymore. Let's try the next prime number
28,927 ÷ 307 = 94.2248 - This has a remainder. 307 is not a factor.
28,927 ÷ 311 = 93.0129 - This has a remainder. 311 is not a factor.
28,927 ÷ 313 = 92.4185 - This has a remainder. 313 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
28,927 ÷ 28,927 = 1 - No remainder! 28,927 is one of the factors!

The orange divisor(s) above are the prime factors of the number 339,024,440. If we put all of it together we have the factors 2 x 2 x 2 x 5 x 293 x 28,927 = 339,024,440. It can also be written in exponential form as 23 x 51 x 2931 x 28,9271.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 339,024,440.

339,024,440
Factor Arrows
2169,512,220
Factor Arrows
284,756,110
Factor Arrows
242,378,055
Factor Arrows
58,475,611
Factor Arrows
29328,927

More Prime Factorization Examples

339,024,438339,024,439339,024,441339,024,442
21 x 32 x 171 x 1,107,9231131 x 231 x 1,133,861131 x 71 x 16,144,021121 x 291 x 471 x 124,3671

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