Q: What is the prime factorization of the number 752,080?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 5 x 7 x 17 x 79
    • or also written as { 2, 2, 2, 2, 5, 7, 17, 79 }
  • Written in exponential form: 24 x 51 x 71 x 171 x 791

Why is the prime factorization of 752,080 written as 24 x 51 x 71 x 171 x 791?

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 752,080

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 752,080 by 2

752,080 ÷ 2 = 376,040 - No remainder! 2 is one of the factors!
376,040 ÷ 2 = 188,020 - No remainder! 2 is one of the factors!
188,020 ÷ 2 = 94,010 - No remainder! 2 is one of the factors!
94,010 ÷ 2 = 47,005 - No remainder! 2 is one of the factors!
47,005 ÷ 2 = 23,502.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
47,005 ÷ 3 = 15,668.3333 - This has a remainder. 3 is not a factor.
47,005 ÷ 5 = 9,401 - No remainder! 5 is one of the factors!
9,401 ÷ 5 = 1,880.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
9,401 ÷ 7 = 1,343 - No remainder! 7 is one of the factors!
1,343 ÷ 7 = 191.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
1,343 ÷ 11 = 122.0909 - This has a remainder. 11 is not a factor.
1,343 ÷ 13 = 103.3077 - This has a remainder. 13 is not a factor.
1,343 ÷ 17 = 79 - No remainder! 17 is one of the factors!
79 ÷ 17 = 4.6471 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
79 ÷ 19 = 4.1579 - This has a remainder. 19 is not a factor.
79 ÷ 23 = 3.4348 - This has a remainder. 23 is not a factor.
79 ÷ 29 = 2.7241 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
79 ÷ 79 = 1 - No remainder! 79 is one of the factors!

The orange divisor(s) above are the prime factors of the number 752,080. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 5 x 7 x 17 x 79 = 752,080. It can also be written in exponential form as 24 x 51 x 71 x 171 x 791.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 752,080.

752,080
Factor Arrows
2376,040
Factor Arrows
2188,020
Factor Arrows
294,010
Factor Arrows
247,005
Factor Arrows
59,401
Factor Arrows
71,343
Factor Arrows
1779

More Prime Factorization Examples

752,078752,079752,081752,082
21 x 376,039131 x 250,6931111 x 68,371121 x 31 x 1631 x 7691

Try the factor calculator

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