Q: What is the prime factorization of the number 871,996?

 A:
  • The prime factors are: 2 x 2 x 277 x 787
    • or also written as { 2, 2, 277, 787 }
  • Written in exponential form: 22 x 2771 x 7871

Why is the prime factorization of 871,996 written as 22 x 2771 x 7871?

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 871,996

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 871,996 by 2

871,996 ÷ 2 = 435,998 - No remainder! 2 is one of the factors!
435,998 ÷ 2 = 217,999 - No remainder! 2 is one of the factors!
217,999 ÷ 2 = 108,999.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
217,999 ÷ 3 = 72,666.3333 - This has a remainder. 3 is not a factor.
217,999 ÷ 5 = 43,599.8 - This has a remainder. 5 is not a factor.
217,999 ÷ 7 = 31,142.7143 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
217,999 ÷ 277 = 787 - No remainder! 277 is one of the factors!
787 ÷ 277 = 2.8412 - There is a remainder. We can't divide by 277 evenly anymore. Let's try the next prime number
787 ÷ 281 = 2.8007 - This has a remainder. 281 is not a factor.
787 ÷ 283 = 2.7809 - This has a remainder. 283 is not a factor.
787 ÷ 293 = 2.686 - This has a remainder. 293 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
787 ÷ 787 = 1 - No remainder! 787 is one of the factors!

The orange divisor(s) above are the prime factors of the number 871,996. If we put all of it together we have the factors 2 x 2 x 277 x 787 = 871,996. It can also be written in exponential form as 22 x 2771 x 7871.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 871,996.

871,996
Factor Arrows
2435,998
Factor Arrows
2217,999
Factor Arrows
277787

More Prime Factorization Examples

871,994871,995871,997871,998
21 x 435,997131 x 51 x 611 x 953171 x 431 x 2,897121 x 31 x 171 x 831 x 1031

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