Q: What is the prime factorization of the number 3,859,440?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 5 x 13 x 1,237
    • or also written as { 2, 2, 2, 2, 3, 5, 13, 1,237 }
  • Written in exponential form: 24 x 31 x 51 x 131 x 1,2371

Why is the prime factorization of 3,859,440 written as 24 x 31 x 51 x 131 x 1,2371?

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 3,859,440

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 3,859,440 by 2

3,859,440 ÷ 2 = 1,929,720 - No remainder! 2 is one of the factors!
1,929,720 ÷ 2 = 964,860 - No remainder! 2 is one of the factors!
964,860 ÷ 2 = 482,430 - No remainder! 2 is one of the factors!
482,430 ÷ 2 = 241,215 - No remainder! 2 is one of the factors!
241,215 ÷ 2 = 120,607.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
241,215 ÷ 3 = 80,405 - No remainder! 3 is one of the factors!
80,405 ÷ 3 = 26,801.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
80,405 ÷ 5 = 16,081 - No remainder! 5 is one of the factors!
16,081 ÷ 5 = 3,216.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
16,081 ÷ 7 = 2,297.2857 - This has a remainder. 7 is not a factor.
16,081 ÷ 11 = 1,461.9091 - This has a remainder. 11 is not a factor.
16,081 ÷ 13 = 1,237 - No remainder! 13 is one of the factors!
1,237 ÷ 13 = 95.1538 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
1,237 ÷ 17 = 72.7647 - This has a remainder. 17 is not a factor.
1,237 ÷ 19 = 65.1053 - This has a remainder. 19 is not a factor.
1,237 ÷ 23 = 53.7826 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,237 ÷ 1,237 = 1 - No remainder! 1,237 is one of the factors!

The orange divisor(s) above are the prime factors of the number 3,859,440. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 5 x 13 x 1,237 = 3,859,440. It can also be written in exponential form as 24 x 31 x 51 x 131 x 1,2371.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 3,859,440.

3,859,440
Factor Arrows
21,929,720
Factor Arrows
2964,860
Factor Arrows
2482,430
Factor Arrows
2241,215
Factor Arrows
380,405
Factor Arrows
516,081
Factor Arrows
131,237

More Prime Factorization Examples

3,859,4383,859,4393,859,4413,859,442
21 x 111 x 311 x 5,65913,859,43912771 x 13,933121 x 171 x 113,5131

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