# Prime Factorization - Examples, Exercises and Solutions

## Prime Factorization

Prime factorization (or prime decomposition) consists of breaking down a certain number into prime numbers, called factors, whose product (multiplication) results in the original number.

### The first method - Factor tree method

Let's take the number we want to factorize and draw $2$ branches from it.
We will ask ourselves, which $2$ numbers can we find whose multiplication results in this same number, except for the original number and $1$.
Let's see if the numbers we found are prime or composite, we will break down the composite ones into two branches again.
We will continue breaking down all the composite numbers until we only have primes, which we will mark with a circle.

### The second method - Split Window Method

Let's write the number we want to factorize on the left side of a vertical line that acts as a division window.
Let's look for the smallest prime number by which we can divide the original, we write it on the right side of the line and the result we write on the left, below the first one. We will continue in this manner until we reach the number $1$ and finish the exercise.
All the prime numbers will appear on the right side of the dividing line.

### Suggested Topics to Practice in Advance

1. Prime Numbers and Composite Numbers

## Examples with solutions for Prime Factorization

### Exercise #1

Write all the factors of the following number: $6$

### Video Solution

$2,3$

### Exercise #2

Write all the factors of the following number: $7$

No prime factors

### Exercise #3

Write all the factors of the following number: $5$

No prime factors

### Exercise #4

Write all the factors of the following number: $9$

### Video Solution

$3,3$

### Exercise #5

Write all the factors of the following number: $8$

### Video Solution

$2,2,2$

### Exercise #6

Write all the factors of the following number: $4$

### Video Solution

$2,2$

### Exercise #7

Write all the factors of the following number: $16$

### Video Solution

$2,2,2,2$

### Exercise #8

Write all the factors of the following number: $12$

### Video Solution

$3,2,2$

### Exercise #9

Write all the factors of the following number: $13$

No prime factors

### Exercise #10

Write all the factors of the following number: $14$

### Video Solution

$2,7$

### Exercise #11

Write all the factors of the following number: $18$

### Video Solution

$2,3,3$

### Exercise #12

Write all the factors of the following number: $26$

### Video Solution

$13,2$

### Exercise #13

Write all the factors of the following number: $31$

No prime factors

### Exercise #14

Write all the factors of the following number: $99$

### Video Solution

$11,3,3$

### Exercise #15

Write all the factors of the following number: $290$

### Video Solution

$5,2,29$