# Q: What is the prime factorization of the number 315,487?

- The prime factors are: 31 x 10,177
- or also written as { 31, 10,177 }

- Written in exponential form: 31
^{1}x 10,177^{1}

A:

- The prime factors are: 31 x 10,177
- or also written as { 31, 10,177 }

- Written in exponential form: 31
^{1}x 10,177^{1}

**Prime factorization** or **prime factor decomposition** is the process of finding which prime numbers can be multiplied together to make the original number.

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.

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 315,487 by 2

315,487 ÷ 2 = 157,743.5 - This has a remainder. Let's try another prime number.

315,487 ÷ 3 = 105,162.3333 - This has a remainder. Let's try another prime number.

315,487 ÷ 5 = 63,097.4 - This has a remainder. Let's try another prime number.

...**Keep trying increasingly larger numbers until you find one that divides evenly.**

...

315,487 ÷ 31 = 10,177 - No remainder! 31 is one of the factors!

10,177 ÷ 31 = 328.2903 - There is a remainder. We can't divide by 31 evenly anymore. Let's try the next prime number

10,177 ÷ 37 = 275.0541 - This has a remainder. 37 is not a factor.

10,177 ÷ 41 = 248.2195 - This has a remainder. 41 is not a factor.

10,177 ÷ 43 = 236.6744 - This has a remainder. 43 is not a factor.

...**Keep trying increasingly larger numbers until you find one that divides evenly.**

...

10,177 ÷ 10,177 = 1 - No remainder! 10,177 is one of the factors!

The orange divisor(s) above are the prime factors of the number 315,487. If we put all of it together we have the factors 31 x 10,177 = 315,487. It can also be written in exponential form as 31^{1} x 10,177^{1}.

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 315,487.

315,487 | ||

31 | 10,177 |

315,485 | 315,486 | 315,487 | 315,488 | 315,489 | 315,490 | 315,491 |

5^{1} x 63,097^{1} | 2^{1} x 3^{2} x 17^{1} x 1,031^{1} | 31^{1} x 10,177^{1} | 2^{5} x 9,859^{1} | 3^{1} x 103^{1} x 1,021^{1} | 2^{1} x 5^{1} x 7^{1} x 4,507^{1} | 11^{1} x 23^{1} x 29^{1} x 43^{1} |

General Questions

Factoring Questions

- What are the factors or divisors of the number 315,487?
- What are the prime factors of the number 315,487?
- What is the total number of factors of the number 315,487?
- What is the total number of prime factors of the number 315,487?
- What is the sum of all factors of the number 315,487 including 315,487?
- What is the sum of all factors of the number 315,487 excluding 315,487?
- What are the factor combinations of the number 315,487?
- What is the prime factorization of the number 315,487?

Calculation Questions

Miscellaneous Questions

- How much data will 315,487 bytes hold in different storage units?
- What is 315,487 in other base number systems?
- How is 315,487 spelled out in other languages or countries?
- How is 315,487 formatted in other languages or countries?
- How is 315,487 formatted as currency in different languages or countries?
- What are the different hash algorithm outputs for 315,487?