Q: What is the prime factorization of the number 804,496?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 7 x 11 x 653
    • or also written as { 2, 2, 2, 2, 7, 11, 653 }
  • Written in exponential form: 24 x 71 x 111 x 6531

Why is the prime factorization of 804,496 written as 24 x 71 x 111 x 6531?

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 804,496

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 804,496 by 2

804,496 ÷ 2 = 402,248 - No remainder! 2 is one of the factors!
402,248 ÷ 2 = 201,124 - No remainder! 2 is one of the factors!
201,124 ÷ 2 = 100,562 - No remainder! 2 is one of the factors!
100,562 ÷ 2 = 50,281 - No remainder! 2 is one of the factors!
50,281 ÷ 2 = 25,140.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
50,281 ÷ 3 = 16,760.3333 - This has a remainder. 3 is not a factor.
50,281 ÷ 5 = 10,056.2 - This has a remainder. 5 is not a factor.
50,281 ÷ 7 = 7,183 - No remainder! 7 is one of the factors!
7,183 ÷ 7 = 1,026.1429 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
7,183 ÷ 11 = 653 - No remainder! 11 is one of the factors!
653 ÷ 11 = 59.3636 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
653 ÷ 13 = 50.2308 - This has a remainder. 13 is not a factor.
653 ÷ 17 = 38.4118 - This has a remainder. 17 is not a factor.
653 ÷ 19 = 34.3684 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
653 ÷ 653 = 1 - No remainder! 653 is one of the factors!

The orange divisor(s) above are the prime factors of the number 804,496. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 7 x 11 x 653 = 804,496. It can also be written in exponential form as 24 x 71 x 111 x 6531.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 804,496.

804,496
Factor Arrows
2402,248
Factor Arrows
2201,124
Factor Arrows
2100,562
Factor Arrows
250,281
Factor Arrows
77,183
Factor Arrows
11653

More Prime Factorization Examples

804,494804,495804,497804,498
21 x 231 x 17,489131 x 51 x 53,6331804,497121 x 31 x 191 x 7,0571

Try the factor calculator

Explore more about the number 804,496:


Ask a Question