# Prime Numbers and Composite Numbers

Prime and composite numbers are the two types of numbers that differ based on the number of factors they have. In this article, we’ll look at the details regarding prime and composite numbers. After that, we will look at some examples and a grid. The grid will help us identify the numbers more easily.

##### ALGEBRA

Relevant for…

Learning to differentiate between prime numbers and composite numbers.

See examples

##### ALGEBRA

Relevant for…

Learning to differentiate between prime numbers and composite numbers.

See examples

## What are prime numbers?

Prime numbers are numbers that have only two divisors. These numbers are only divisible by 1 and by themselves. This means that if we try to divide the number by any number other than 1 or itself, we will get a remainder.

Keep in mind that 1 is not considered a prime number.

## Exercises with prime and composite numbers

We can use the following exercises to better understand prime numbers:

### EXERCISES

• Lorraine has 6 cherries and wants to share them, but she does not know how many people she can share them with so that each one receives the same amount and there is no leftover. How many ways are there to do this?

Here’s Lorraine and her 6 cherries:

How can we divide them?

The first and easiest way is to give them to one person, that is, divide by 1. In this way, one person receives all 6 cherries.

The next option is to divide them between 2 people. In this way, each person receives 3 cherries:

We are going to continue with the next number, 3. If we divide 6 cherries for 3 people, this is an exact division and each person receives 2 cherries:

Continuing with the numbers, we do not obtain exact divisions with 4 and 5, but with 6. Since 6 divided by 6 is 1, if we give the cherries to 6 people, each one receives 1 cherry:

Therefore, we have 6 cherries that we can share with an exact division between 1, 2, 3, and 6 people. That is, we can divide the number 6 by 1, 2, 3, and 6 to get no remainder. These numbers are known as the factors of 6.

• Now let’s try the number 7. Lorraine has 7 cherries and she wants to share them, but she does not know how many people she can share them with so that each one receives the same amount and there is no leftover. How many ways are there to do this?

Carlos is lucky as he received all the cherries.

Are there other ways to divide? We can’t divide 7 by 2, 3, 4, 5, or 6, but we can divide by 7.

Lorraine can share the cherries with 7 people by giving 1 to each:

We can see that 7 can only be divided by 1 and 7, its divisors are 1 and 7. These types of numbers are called prime numbers.

Let’s find more prime numbers:

• Is 4 a prime number?

No, its divisors are 1, 2 and 4.

• Is 5 a prime number?

Yes, its divisors are 1 and 5.

• Is 10 a prime number?

No, its divisors are 1, 5 and 10.

With this you can determine if a certain number is prime or not.

## What is the importance of prime numbers?

Prime numbers are the basis of arithmetic since any number consists of a product made up of a series of these numbers.

Prime numbers are very relevant in several areas because they have very important properties for factoring. One of those properties is that, while it is easy to find large prime numbers, it is inevitably difficult to factor large numbers back to primes.

It is one thing to find that 20 is equal to (2 * 2 * 5), but it is something else to find that 2,244,354 is (2 * 3 * 7 * 53,437). It is for this reason that prime numbers are vital in electronic communications. Most of modern computer cryptography works using prime factors of large numbers.

Prime numbers ​​are important to mathematicians because they are the basis of whole numbers, and they are important to computing because their strange mathematical properties make them perfect for our current encryption uses.

## What are composite numbers?

Let’s look at examples of prime and composite numbers:

7 can be written as the multiplication of 1 and 7, but it cannot be written as any other multiplication of natural numbers. 7 only has the divisors 1 and 7, therefore it is a prime number.

12 can be written as the multiplication of 1 and 12, as well as the multiplication of 2 and 6, 3 and 4. Since 12 is divisible by more numbers other than 1 and itself, 12 is a composite number.

### Is 1 a prime number?

It is reasonable to think that if 1 can only be divided by 1 and by itself, 1 is prime. However, 1 is not considered a prime number since it actually only has one divisor. The criterion “an integer is prime only if it has two positive divisors” is used in this argument.

If the number 1 was considered a prime, then the mathematical properties would have to be rethought.

### Is 1 a composite number?

1 is not a composite number since it cannot be formed as the product of prime numbers. So the number 1 is neither prime nor composite.

## Examples of prime and composite numbers

In the following table, we have the numbers from 1 to 13 along with their divisors. The divisors which are different from 1 and the number itself are highlighted:  