# Prime Numbers and Composite Numbers

🏆Practice prime numbers and composite numbers

## Definitions of Prime Numbers and Composite Numbers

### Prime number

A prime number is a natural number that is divisible only by itself and by $1$.

### Composite number

A composite number is a number that can be written as the product of two natural numbers smaller than it, with the exception of $1$ and itself.

The number $1$ –> is a special number that is neither prime nor composite.
The number $2$ –> is the only even number that is prime.

## Test yourself on prime numbers and composite numbers!

Is the number equal to $$n$$ prime or composite?

$$n=10$$

## What are prime numbers and composite numbers?

In this article, we will describe what exactly prime and composite numbers are; we will learn to identify them and get to know special numbers.

### What is a prime number?

A prime number is a natural number divisible only by itself and by $1$.
This means that, when we talk about a prime number, we cannot find any other two numbers besides itself and $1$, that when multiplied together give us that number as a product.
For example: the number $3$
$3$ is a prime number. It can be divided only by $3$ and by $1$.
Even if we want to write it as a multiplication, this will only be with the factors $1$ and $3$ and not with natural numbers smaller than it.

Another example: the number $13$
This number is divisible only by itself and by $1$ and we cannot write it as the product of two natural numbers smaller than it, except for $1$ and $13$.

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### What is a composite number?

A composite number is a number that can be written as the product of two natural numbers smaller than it, except for $1$ and itself.
A composite number can be expressed as the product of itself and $1$ clearly, but always with two other factors that do not equal $1$.
For example: the number $8$
$8$ is a composite number. It can be represented as the product of $4$ and $2$.
Another example: the number $6$
$6$ is a composite number. $6$ can be represented as the product of $3$ and $2$.

In summary
When you need to determine if a certain number is prime or composite, ask yourself:
Is said number divisible by other divisors besides itself and $1$? Can we represent it as the product of natural numbers smaller than it, outside of $1$ and the number itself?
If the answer is yes the number is composite
If the answer is no the number is prime

Valuable fact: Every even number is composite, except for $2$.

### Exercises on Prime or Composite Numbers

Determine if the following numbers are prime or composite:
The number $7$
Solution: $7$ is a prime number. It can only be represented as the product of $7$ and $1$.
The number $5$
Solution: The number $5$ is prime. It can only be represented with the natural numbers $1$ and $5$.
The number $20$
Solution: The number $20$ is composite. It can be represented as the product of $10$ and $2$, or $4$ and $5$.
Pay attention –> The number $20$ can also be represented as the product of $3$ factors –> $2*2*5$
and, clearly, it is considered composite.

Do you know what the answer is?

### Special Numbers

Now we are going to introduce you to some very special numbers! Numbers that might make you think more than once before you can determine if they are prime or composite:
The number $1$ –> Is neither prime nor composite.
The number $1$ Is divisible only by $1$ which, in fact, is itself. It can only be represented through the multiplication of $1$ and $1$, making it a number that is neither prime nor composite.
The number $2$ –> is prime.
$2$ can be divided only by itself and by $1$ this makes it a prime number as dictated by its definition.
So why is it considered special?
All even numbers are composite except for $2$! All even numbers are divisible by $2$ and another number. But, when it itself is $2$, that's another matter.

### More exercises

Determine if the following numbers are prime or composite:
The number $39$
Solution: it is a composite number. It can be represented as the product of $13$ and $3$.
The number $17$
Solution: it is a prime number. It is divisible only by $1$ and itself.
The number $57$
Solution: it is a composite number. It can be represented as the product of $3$ and $19$.

The number $19$
Solution: it is a prime number. It is divisible only by $1$ and itself.

## Examples and exercises with solutions of prime numbers and composite numbers

### Exercise #1

Is the number equal to $n$ prime or composite?

$n=10$

Composite

### Exercise #2

Is the number equal to $n$ prime or composite?

$n=42$

Composite

### Exercise #3

Is the number equal to $n$ prime or composite?

$n=20$

Composite

### Exercise #4

Is the number equal to $n$ prime or composite?

$n=36$

Composite

### Exercise #5

Is the number equal to $n$ prime or composite?

$n=22$