Q: What is the prime factorization of the number 884,770?

 A:
  • The prime factors are: 2 x 5 x 103 x 859
    • or also written as { 2, 5, 103, 859 }
  • Written in exponential form: 21 x 51 x 1031 x 8591

Why is the prime factorization of 884,770 written as 21 x 51 x 1031 x 8591?

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 884,770

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 884,770 by 2

884,770 ÷ 2 = 442,385 - No remainder! 2 is one of the factors!
442,385 ÷ 2 = 221,192.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
442,385 ÷ 3 = 147,461.6667 - This has a remainder. 3 is not a factor.
442,385 ÷ 5 = 88,477 - No remainder! 5 is one of the factors!
88,477 ÷ 5 = 17,695.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
88,477 ÷ 7 = 12,639.5714 - This has a remainder. 7 is not a factor.
88,477 ÷ 11 = 8,043.3636 - This has a remainder. 11 is not a factor.
88,477 ÷ 13 = 6,805.9231 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
88,477 ÷ 103 = 859 - No remainder! 103 is one of the factors!
859 ÷ 103 = 8.3398 - There is a remainder. We can't divide by 103 evenly anymore. Let's try the next prime number
859 ÷ 107 = 8.028 - This has a remainder. 107 is not a factor.
859 ÷ 109 = 7.8807 - This has a remainder. 109 is not a factor.
859 ÷ 113 = 7.6018 - This has a remainder. 113 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
859 ÷ 859 = 1 - No remainder! 859 is one of the factors!

The orange divisor(s) above are the prime factors of the number 884,770. If we put all of it together we have the factors 2 x 5 x 103 x 859 = 884,770. It can also be written in exponential form as 21 x 51 x 1031 x 8591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 884,770.

884,770
Factor Arrows
2442,385
Factor Arrows
588,477
Factor Arrows
103859

More Prime Factorization Examples

884,768884,769884,771884,772
25 x 431 x 643131 x 294,9231311 x 28,541122 x 32 x 71 x 3,5111

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