Q: What is the prime factorization of the number 6,589,440?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 13
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 11, 13 }
  • Written in exponential form: 210 x 32 x 51 x 111 x 131

Why is the prime factorization of 6,589,440 written as 210 x 32 x 51 x 111 x 131?

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 6,589,440

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 6,589,440 by 2

6,589,440 ÷ 2 = 3,294,720 - No remainder! 2 is one of the factors!
3,294,720 ÷ 2 = 1,647,360 - No remainder! 2 is one of the factors!
1,647,360 ÷ 2 = 823,680 - No remainder! 2 is one of the factors!
823,680 ÷ 2 = 411,840 - No remainder! 2 is one of the factors!
411,840 ÷ 2 = 205,920 - No remainder! 2 is one of the factors!
205,920 ÷ 2 = 102,960 - No remainder! 2 is one of the factors!
102,960 ÷ 2 = 51,480 - No remainder! 2 is one of the factors!
51,480 ÷ 2 = 25,740 - No remainder! 2 is one of the factors!
25,740 ÷ 2 = 12,870 - No remainder! 2 is one of the factors!
12,870 ÷ 2 = 6,435 - No remainder! 2 is one of the factors!
6,435 ÷ 2 = 3,217.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
6,435 ÷ 3 = 2,145 - No remainder! 3 is one of the factors!
2,145 ÷ 3 = 715 - No remainder! 3 is one of the factors!
715 ÷ 3 = 238.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
715 ÷ 5 = 143 - No remainder! 5 is one of the factors!
143 ÷ 5 = 28.6 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
143 ÷ 7 = 20.4286 - This has a remainder. 7 is not a factor.
143 ÷ 11 = 13 - No remainder! 11 is one of the factors!
13 ÷ 11 = 1.1818 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 6,589,440. 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 2 x 3 x 3 x 5 x 11 x 13 = 6,589,440. It can also be written in exponential form as 210 x 32 x 51 x 111 x 131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 6,589,440.

6,589,440
Factor Arrows
23,294,720
Factor Arrows
21,647,360
Factor Arrows
2823,680
Factor Arrows
2411,840
Factor Arrows
2205,920
Factor Arrows
2102,960
Factor Arrows
251,480
Factor Arrows
225,740
Factor Arrows
212,870
Factor Arrows
26,435
Factor Arrows
32,145
Factor Arrows
3715
Factor Arrows
5143
Factor Arrows
1113

More Prime Factorization Examples

6,589,4386,589,4396,589,4416,589,442
21 x 171 x 291 x 411 x 1631711 x 92,8091371 x 178,093121 x 1011 x 32,6211

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