Prime numbers are numbers that are only divisible by 1 and by themselves. It is possible to determine whether a number is prime or not by dividing it by several prime numbers and finding some other number that divides it without leaving a remainder.

In this article, we will look at a summary of prime and composite numbers. In addition, we will solve several problems to determine if a given number is prime or composite.

## Summary of prime and composite numbers

Remember that prime numbers are numbers that can only be divided by 1 and by themselves. For example, 5 is a prime number since it can only be divided by 1 and 5.

On the other hand, composite numbers are those numbers that can be divided by 1, by itself, and at least by another number more. For example, 8 is a composite number since it can be divided by 1, 2, 4, and 8.

To determine if a number is prime or composite, we have to divide it by prime numbers to find out if there is another number for which it is divisible. It is advisable to try from the smallest prime numbers.

For example, we try to divide the number in question by 2, 3, 5, 7, 11, 13, 17, 19 in that order. If the number can be divided by these numbers, then it is not a prime number.

Therefore, the important thing here is that we must memorize the first prime numbers, and then use these numbers and determine if another number is prime or composite.

### Number 1

Now let’s look at the number 1. We know that the rule for a number to be prime is that it be divisible only by 1 and by itself. However, the full definition of a prime number is that a prime is a number greater than 1 that is divisible only by 1 and by itself. Therefore, 1 is not a prime number. This is because 1 does not have two divisors.

## Prime and composite numbers – Examples with answers

The following prime and composite number examples apply knowledge of number divisibility to determine whether a given number is prime or composite. These examples have their respective solution to understand the process used.

#### EXAMPLE 1

Determine whether 9 is a prime number or a composite number.

##### Solution

We have to divide 9 by prime numbers to find out if there is another number that is divisible by.

Therefore, we start with 2. If we divide 9 by 2, we get 4.5. This means that 2 is not a factor of 9. If we divide 9 by 3, we get 3. We got a whole number, so 3 is a factor of 9.

Because 9 is divisible by 3, 9 is a composite number since it is divisible by 1, 9, and at least one other number.

#### EXAMPLE 2

Determine whether 23 is a prime number or a composite number.

##### Solution

We divide 23 by different prime numbers to find out if it is divisible by another number.

We start by dividing it by 2. By dividing it by 2, we don’t get a whole number, nor do we get a whole number if we divide it by 3, or by 5, or by 7, or by 11.

We see that there is no other integer that divides 23 without leaving a remainder. This means that 23 is a prime number.

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#### EXAMPLE 3

Determine whether 33 is a prime number or a composite number.

##### Solution

We start by dividing 33 by 2. By doing this, we get 16.5, so it is not divisible by 2. Then, we divide by 3. We get 11, so it is divisible by 3.

This means that 33 is a composite number since it is divisible by at least one other number other than 1 and itself.

#### EXAMPLE 4

Determine whether 64 is a prime number or a composite number.

##### Solution

Quickly, we can determine that this number is divisible by 2. Thus, 64 is a composite number since it is divisible by 1 by itself and by at least one other number.

Something important to remember is that all even numbers greater than 2 are composite numbers since all even numbers are divisible by 2.

#### EXAMPLE 5

Determine whether 41 is a prime number or a composite number.

##### Solution

We start by dividing by 2. By dividing by 2, we get 20.5, so it is not divisible by 2. Then we try 3, 5, 7, 11, 13, 17. None of these numbers divides 41 exactly, so there is no other number by which 41 is divisible.

Therefore, 41 is a prime number.

## Prime and composite numbers – Practice problems

Solve the following exercises to practice your knowledge of prime and composite numbers. If you have problems with these exercises, you can look at the solved exercises above to follow the process used.

## See also

Interested in learning more about algebraic topics? Take a look at these pages:

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