Q: What is the prime factorization of the number 315,488?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 9,859
    • or also written as { 2, 2, 2, 2, 2, 9,859 }
  • Written in exponential form: 25 x 9,8591

Why is the prime factorization of 315,488 written as 25 x 9,8591?

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 315,488

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 315,488 by 2

315,488 ÷ 2 = 157,744 - No remainder! 2 is one of the factors!
157,744 ÷ 2 = 78,872 - No remainder! 2 is one of the factors!
78,872 ÷ 2 = 39,436 - No remainder! 2 is one of the factors!
39,436 ÷ 2 = 19,718 - No remainder! 2 is one of the factors!
19,718 ÷ 2 = 9,859 - No remainder! 2 is one of the factors!
9,859 ÷ 2 = 4,929.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
9,859 ÷ 3 = 3,286.3333 - This has a remainder. 3 is not a factor.
9,859 ÷ 5 = 1,971.8 - This has a remainder. 5 is not a factor.
9,859 ÷ 7 = 1,408.4286 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
9,859 ÷ 9,859 = 1 - No remainder! 9,859 is one of the factors!

The orange divisor(s) above are the prime factors of the number 315,488. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 9,859 = 315,488. It can also be written in exponential form as 25 x 9,8591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 315,488.

315,488
Factor Arrows
2157,744
Factor Arrows
278,872
Factor Arrows
239,436
Factor Arrows
219,718
Factor Arrows
29,859

More Prime Factorization Examples

315,486315,487315,489315,490
21 x 32 x 171 x 1,0311311 x 10,177131 x 1031 x 1,021121 x 51 x 71 x 4,5071

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