# Q: What is the prime factorization of the number 398,546?

- The prime factors are: 2 x 101 x 1,973
- or also written as { 2, 101, 1,973 }

- Written in exponential form: 2
^{1}x 101^{1}x 1,973^{1}

A:

- The prime factors are: 2 x 101 x 1,973
- or also written as { 2, 101, 1,973 }

- Written in exponential form: 2
^{1}x 101^{1}x 1,973^{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 398,546 by 2

398,546 ÷ 2 = 199,273 - No remainder! 2 is one of the factors!

199,273 ÷ 2 = 99,636.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number

199,273 ÷ 3 = 66,424.3333 - This has a remainder. 3 is not a factor.

199,273 ÷ 5 = 39,854.6 - This has a remainder. 5 is not a factor.

199,273 ÷ 7 = 28,467.5714 - This has a remainder. 7 is not a factor.

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

...

199,273 ÷ 101 = 1,973 - No remainder! 101 is one of the factors!

1,973 ÷ 101 = 19.5347 - There is a remainder. We can't divide by 101 evenly anymore. Let's try the next prime number

1,973 ÷ 103 = 19.1553 - This has a remainder. 103 is not a factor.

1,973 ÷ 107 = 18.4393 - This has a remainder. 107 is not a factor.

1,973 ÷ 109 = 18.1009 - This has a remainder. 109 is not a factor.

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

...

1,973 ÷ 1,973 = 1 - No remainder! 1,973 is one of the factors!

The orange divisor(s) above are the prime factors of the number 398,546. If we put all of it together we have the factors 2 x 101 x 1,973 = 398,546. It can also be written in exponential form as 2^{1} x 101^{1} x 1,973^{1}.

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 398,546.

398,546 | |||

2 | 199,273 | ||

101 | 1,973 |

398,544 | 398,545 | 398,547 | 398,548 |

2^{4} x 3^{1} x 19^{2} x 23^{1} | 5^{1} x 7^{1} x 59^{1} x 193^{1} | 3^{3} x 29^{1} x 509^{1} | 2^{2} x 17^{1} x 5,861^{1} |

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General Questions

- How is the number 398,546 written in scientific notation?
- What is the absolute value of the number 398,546?
- What is the negative version of the number 398,546?
- What is the place value chart for the number 398,546?
- What is the digital root of the number 398,546?
- How many digits is in the number 398,546?
- How is 398,546 written in roman numerals?

Factoring Questions

- What are the factors or divisors of the number 398,546?
- What are the prime factors of the number 398,546?
- What is the total number of factors of the number 398,546?
- What is the total number of prime factors of the number 398,546?
- What is the sum of all factors of the number 398,546 including 398,546?
- What is the sum of all factors of the number 398,546 excluding 398,546?
- What are the factor combinations of the number 398,546?
- What is the prime factorization of the number 398,546?

Calculation Questions

Miscellaneous Questions

- How much data will 398,546 bytes hold in different storage units?
- What is 398,546 in other base number systems?
- How is 398,546 spelled out in other languages or countries?
- How is 398,546 formatted in other languages or countries?
- How is 398,546 formatted as currency in different languages or countries?
- What are the different hash algorithm outputs for 398,546?