Q: What is the prime factorization of the number 868,992?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 31 x 73
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 3, 31, 73 }
  • Written in exponential form: 27 x 31 x 311 x 731

Why is the prime factorization of 868,992 written as 27 x 31 x 311 x 731?

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 868,992

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 868,992 by 2

868,992 ÷ 2 = 434,496 - No remainder! 2 is one of the factors!
434,496 ÷ 2 = 217,248 - No remainder! 2 is one of the factors!
217,248 ÷ 2 = 108,624 - No remainder! 2 is one of the factors!
108,624 ÷ 2 = 54,312 - No remainder! 2 is one of the factors!
54,312 ÷ 2 = 27,156 - No remainder! 2 is one of the factors!
27,156 ÷ 2 = 13,578 - No remainder! 2 is one of the factors!
13,578 ÷ 2 = 6,789 - No remainder! 2 is one of the factors!
6,789 ÷ 2 = 3,394.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
6,789 ÷ 3 = 2,263 - No remainder! 3 is one of the factors!
2,263 ÷ 3 = 754.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
2,263 ÷ 5 = 452.6 - This has a remainder. 5 is not a factor.
2,263 ÷ 7 = 323.2857 - This has a remainder. 7 is not a factor.
2,263 ÷ 11 = 205.7273 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,263 ÷ 31 = 73 - No remainder! 31 is one of the factors!
73 ÷ 31 = 2.3548 - There is a remainder. We can't divide by 31 evenly anymore. Let's try the next prime number
73 ÷ 37 = 1.973 - This has a remainder. 37 is not a factor.
73 ÷ 41 = 1.7805 - This has a remainder. 41 is not a factor.
73 ÷ 43 = 1.6977 - This has a remainder. 43 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
73 ÷ 73 = 1 - No remainder! 73 is one of the factors!

The orange divisor(s) above are the prime factors of the number 868,992. 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 3 x 31 x 73 = 868,992. It can also be written in exponential form as 27 x 31 x 311 x 731.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 868,992.

868,992
Factor Arrows
2434,496
Factor Arrows
2217,248
Factor Arrows
2108,624
Factor Arrows
254,312
Factor Arrows
227,156
Factor Arrows
213,578
Factor Arrows
26,789
Factor Arrows
32,263
Factor Arrows
3173

More Prime Factorization Examples

868,990868,991868,993868,994
21 x 51 x 671 x 1,29711371 x 6,3431868,993121 x 71 x 62,0711

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