# Q: What is the prime factorization of the number 123,456,789?

- The prime factors are: 3 x 3 x 3,607 x 3,803
- or also written as { 3, 3, 3,607, 3,803 }

- Written in exponential form: 3
^{2}x 3,607^{1}x 3,803^{1}

A:

- The prime factors are: 3 x 3 x 3,607 x 3,803
- or also written as { 3, 3, 3,607, 3,803 }

- Written in exponential form: 3
^{2}x 3,607^{1}x 3,803^{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 123,456,789 by 2

123,456,789 ÷ 2 = 61,728,394.5 - This has a remainder. Let's try another prime number.

123,456,789 ÷ 3 = 41,152,263 - No remainder! 3 is one of the factors!

41,152,263 ÷ 3 = 13,717,421 - No remainder! 3 is one of the factors!

13,717,421 ÷ 3 = 4,572,473.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number

13,717,421 ÷ 5 = 2,743,484.2 - This has a remainder. 5 is not a factor.

13,717,421 ÷ 7 = 1,959,631.5714 - This has a remainder. 7 is not a factor.

13,717,421 ÷ 11 = 1,247,038.2727 - This has a remainder. 11 is not a factor.

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

...

13,717,421 ÷ 3,607 = 3,803 - No remainder! 3,607 is one of the factors!

3,803 ÷ 3,607 = 1.0543 - There is a remainder. We can't divide by 3607 evenly anymore. Let's try the next prime number

3,803 ÷ 3,613 = 1.0526 - This has a remainder. 3,613 is not a factor.

3,803 ÷ 3,617 = 1.0514 - This has a remainder. 3,617 is not a factor.

3,803 ÷ 3,623 = 1.0497 - This has a remainder. 3,623 is not a factor.

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

...

3,803 ÷ 3,803 = 1 - No remainder! 3,803 is one of the factors!

The orange divisor(s) above are the prime factors of the number 123,456,789. If we put all of it together we have the factors 3 x 3 x 3,607 x 3,803 = 123,456,789. It can also be written in exponential form as 3^{2} x 3,607^{1} x 3,803^{1}.

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 123,456,789.

123,456,789 | ||||

3 | 41,152,263 | |||

3 | 13,717,421 | |||

3,607 | 3,803 |

123,456,787 | 123,456,788 | 123,456,790 | 123,456,791 |

31^{2} x 128,467^{1} | 2^{2} x 7^{1} x 13^{1} x 17^{1} x 71^{1} x 281^{1} | 2^{1} x 5^{1} x 37^{1} x 333,667^{1} | 123,456,791^{1} |

General Questions

Factoring Questions

- What are the factors or divisors of the number 123,456,789?
- What are the prime factors of the number 123,456,789?
- What is the total number of factors of the number 123,456,789?
- What is the total number of prime factors of the number 123,456,789?
- What is the sum of all factors of the number 123,456,789 including 123,456,789?
- What is the sum of all factors of the number 123,456,789 excluding 123,456,789?
- What are the factor combinations of the number 123,456,789?
- What is the prime factorization of the number 123,456,789?

Calculation Questions

Miscellaneous Questions

- How much data will 123,456,789 bytes hold in different storage units?
- What is 123,456,789 in other base number systems?
- How is 123,456,789 spelled out in other languages or countries?
- How is 123,456,789 formatted in other languages or countries?
- How is 123,456,789 formatted as currency in different languages or countries?
- What are the different hash algorithm outputs for 123,456,789?