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

### What is prime factorization?

**Prime factorization** or **prime variable decomposition** is the process of recognize which prime numbers have the right to be multiplied with each other to make the original number.

### Finding the prime components of 39

To find the prime factors, you begin by separating the number by the very first prime number, which is 2. If over there **is not** a remainder, an interpretation you deserve to divide evenly, climate 2 is a element of the number. Continue dividing by 2 until you cannot division evenly anymore. Write down how numerous 2"s you were able to divide by evenly. Now shot dividing by the next prime factor, i m sorry is 3. The goal is to get to a quotient of 1.

If that doesn"t make feeling yet, let"s shot it...

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

Let"s start by splitting 39 through 2

39 ÷ 2 = 19.5 - This has actually a remainder. Let"s try another prime number.39 ÷ 3 = 13 - No remainder! 3 is one of the factors!13 ÷ 3 = 4.3333 - over there is a remainder. We can"t divide by 3 evenly anymore. Let"s shot the following prime number13 ÷ 5 = 2.6 - This has actually 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 actually a remainder. 11 is not a factor.13 ÷ 13 = 1 - No remainder! 13 is just one of the factors!

The orange divisor(s) above are the prime factors of the number 39. If we put every one of it with each other we have the components 3 x 13 = 39. It can likewise be created in exponential type as 31 x 131.

### Factor Tree

Another method to execute prime factorization is to usage a factor tree. Below is a element 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 aspect calculator

### Explore more about the number 39:

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