Q: What is the prime factorization of the number 814,716?

 A:
  • The prime factors are: 2 x 2 x 3 x 3 x 7 x 53 x 61
    • or also written as { 2, 2, 3, 3, 7, 53, 61 }
  • Written in exponential form: 22 x 32 x 71 x 531 x 611

Why is the prime factorization of 814,716 written as 22 x 32 x 71 x 531 x 611?

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 814,716

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 814,716 by 2

814,716 ÷ 2 = 407,358 - No remainder! 2 is one of the factors!
407,358 ÷ 2 = 203,679 - No remainder! 2 is one of the factors!
203,679 ÷ 2 = 101,839.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
203,679 ÷ 3 = 67,893 - No remainder! 3 is one of the factors!
67,893 ÷ 3 = 22,631 - No remainder! 3 is one of the factors!
22,631 ÷ 3 = 7,543.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
22,631 ÷ 5 = 4,526.2 - This has a remainder. 5 is not a factor.
22,631 ÷ 7 = 3,233 - No remainder! 7 is one of the factors!
3,233 ÷ 7 = 461.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
3,233 ÷ 11 = 293.9091 - This has a remainder. 11 is not a factor.
3,233 ÷ 13 = 248.6923 - This has a remainder. 13 is not a factor.
3,233 ÷ 17 = 190.1765 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,233 ÷ 53 = 61 - No remainder! 53 is one of the factors!
61 ÷ 53 = 1.1509 - There is a remainder. We can't divide by 53 evenly anymore. Let's try the next prime number
61 ÷ 59 = 1.0339 - This has a remainder. 59 is not a factor.
61 ÷ 61 = 1 - No remainder! 61 is one of the factors!

The orange divisor(s) above are the prime factors of the number 814,716. If we put all of it together we have the factors 2 x 2 x 3 x 3 x 7 x 53 x 61 = 814,716. It can also be written in exponential form as 22 x 32 x 71 x 531 x 611.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 814,716.

814,716
Factor Arrows
2407,358
Factor Arrows
2203,679
Factor Arrows
367,893
Factor Arrows
322,631
Factor Arrows
73,233
Factor Arrows
5361

More Prime Factorization Examples

814,714814,715814,717814,718
21 x 407,357151 x 111 x 14,8131814,717121 x 407,3591

Try the factor calculator

Explore more about the number 814,716:


Ask a Question