Q: What is the prime factorization of the number 809,760?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 241
    • or also written as { 2, 2, 2, 2, 2, 3, 5, 7, 241 }
  • Written in exponential form: 25 x 31 x 51 x 71 x 2411

Why is the prime factorization of 809,760 written as 25 x 31 x 51 x 71 x 2411?

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 809,760

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 809,760 by 2

809,760 ÷ 2 = 404,880 - No remainder! 2 is one of the factors!
404,880 ÷ 2 = 202,440 - No remainder! 2 is one of the factors!
202,440 ÷ 2 = 101,220 - No remainder! 2 is one of the factors!
101,220 ÷ 2 = 50,610 - No remainder! 2 is one of the factors!
50,610 ÷ 2 = 25,305 - No remainder! 2 is one of the factors!
25,305 ÷ 2 = 12,652.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
25,305 ÷ 3 = 8,435 - No remainder! 3 is one of the factors!
8,435 ÷ 3 = 2,811.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
8,435 ÷ 5 = 1,687 - No remainder! 5 is one of the factors!
1,687 ÷ 5 = 337.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
1,687 ÷ 7 = 241 - No remainder! 7 is one of the factors!
241 ÷ 7 = 34.4286 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
241 ÷ 11 = 21.9091 - This has a remainder. 11 is not a factor.
241 ÷ 13 = 18.5385 - This has a remainder. 13 is not a factor.
241 ÷ 17 = 14.1765 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
241 ÷ 241 = 1 - No remainder! 241 is one of the factors!

The orange divisor(s) above are the prime factors of the number 809,760. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 241 = 809,760. It can also be written in exponential form as 25 x 31 x 51 x 71 x 2411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 809,760.

809,760
Factor Arrows
2404,880
Factor Arrows
2202,440
Factor Arrows
2101,220
Factor Arrows
250,610
Factor Arrows
225,305
Factor Arrows
38,435
Factor Arrows
51,687
Factor Arrows
7241

More Prime Factorization Examples

809,758809,759809,761809,762
21 x 1131 x 3,5831809,7591171 x 191 x 231 x 109121 x 671 x 6,0431

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