# Prime Factorization with Exponents - Examples, Exercises and Solutions

## What does it mean?

Any natural number that is not prime can be factorized as a product of prime numbers. This process is known as breaking down numbers into prime factors.

From time to time, to solve a certain exercise in a simpler way, we will have to dfactorize the numbers we are given, and rewrite them as products of prime numbers. This factorization gives the possibility to use the numbers in a more comfortable way, for example, by taking advantage of the properties of powers or exponent laws.

For example:
The number $8$ can be written as $2^3$
The number $1176$ can be also written as $2^2\times3\times7^2$

### Suggested Topics to Practice in Advance

1. Prime Numbers and Composite Numbers

## Examples with solutions for Prime Factorization with Exponents

### 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

$5,2,29$