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## Why is the prime factorization of 39 written as 31 x 131?

### 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 39

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 39 by 2

39 ÷ 2 = 19.5 - This has a remainder. Let"s try another prime number.39 ÷ 3 = 13 - No remainder! 3 is one of the factors!13 ÷ 3 = 4.3333 - There is a remainder. We can"t divide by 3 evenly anymore. Let"s try the next prime number13 ÷ 5 = 2.6 - This has a remainder. 5 is not a factor.13 ÷ 7 = 1.8571 - This has a remainder. 7 is not a factor.13 ÷ 11 = 1.1818 - This has a remainder. 11 is not a factor.13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 39. If we put all of it together we have the factors 3 x 13 = 39. It can also be written in exponential form as 31 x 131.

### Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 39.

39 | ||

3 | 13 |

### More Prime Factorization Examples

37 | 38 | 40 | 41 |

371 | 21 x 191 | 23 x 51 | 411 |

Try the factor calculator

### Explore more about the number 39:

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