Prime Numbers and Composite Numbers

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Definitions of Prime Numbers and Composite Numbers

Prime number

A prime number is a natural number that is divisible only by itself and by 11.

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 11 and itself.

The number 11 –> is a special number that is neither prime nor composite.
The number 22 –> is the only even number that is prime.

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Which of the numbers is a prime number?

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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 11.
This means that, when we talk about a prime number, we cannot find any other two numbers besides itself and 11, that when multiplied together give us that number as a product.
For example: the number 33
33 is a prime number. It can be divided only by 33 and by 11.
Even if we want to write it as a multiplication, this will only be with the factors 11 and 33 and not with natural numbers smaller than it.

Another example: the number 1313
This number is divisible only by itself and by 11 and we cannot write it as the product of two natural numbers smaller than it, except for 11 and 1313.


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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 11 and itself.
A composite number can be expressed as the product of itself and 11 clearly, but always with two other factors that do not equal 11.
For example: the number 88
88 is a composite number. It can be represented as the product of 44 and 22.
Another example: the number 66
66 is a composite number. 66 can be represented as the product of 33 and 22.

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 11? Can we represent it as the product of natural numbers smaller than it, outside of 11 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 22.


Exercises on Prime or Composite Numbers

Determine if the following numbers are prime or composite:
The number 77
Solution: 77 is a prime number. It can only be represented as the product of 77 and 11.
The number 55
Solution: The number 55 is prime. It can only be represented with the natural numbers 11 and 55.
The number 2020
Solution: The number 2020 is composite. It can be represented as the product of 1010 and 22, or 44 and 55.
Pay attention –> The number 2020 can also be represented as the product of 33 factors –> 2∗2∗52*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 11 –> Is neither prime nor composite.
The number 11 Is divisible only by 11 which, in fact, is itself. It can only be represented through the multiplication of 11 and 11, making it a number that is neither prime nor composite.
The number 22 –> is prime.
22 can be divided only by itself and by 11 this makes it a prime number as dictated by its definition.
So why is it considered special?
All even numbers are composite except for 22! All even numbers are divisible by 22 and another number. But, when it itself is 22, that's another matter.


More exercises

Determine if the following numbers are prime or composite:
The number 3939
Solution: it is a composite number. It can be represented as the product of 1313 and 33.
The number 1717
Solution: it is a prime number. It is divisible only by 11 and itself.
The number 5757
Solution: it is a composite number. It can be represented as the product of 33 and 1919.

The number 1919
Solution: it is a prime number. It is divisible only by 11 and itself.


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