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What Are Prime And Composite Numbers?

Whenever you perform factorisation on any number, it is important to know whether it is a prime or composite number. 

To determine this, you need to understand the concept of  Prime Numbers and Composite Numbers and how you can check whether a number is prime or composite. 

What Are Prime Numbers?

A number that has only two factors is called a prime number. The factors of a number are the number that should divide a number to give 0 as the remainder. Prime numbers are numbers, which can be divided by only 1 or the number itself. The prime numbers are mostly the odd numbers; only 2 is an exception. 

Moreover, 2 is an even prime number, and there is no other number included in the prime numbers, which is also even. You must know that 0 and 1 are not prime numbers.

You should also know that no prime ends with 5, except 5. This is because the number that ends with 5 and is greater than the first four prime numbers is easy to divide by 5. This is why they are not included in prime numbers.

Examples Of Prime Number

Though being an odd number, 1 is not considered in the prime numbers. And then comes the next odd, which is 3 — it is the prime number because you can divide 3 by only 2 numbers, which is 1 and the number itself.  

Similarly, this rule can be applied to filter out more prime numbers. Therefore, the prime numbers are 2 ( exceptional ), 3, 5, 7, 11, 13, 17, 19… so on. 

What Are Composite Numbers?

The number, which is not a prime number, is called a Composite number. Composite numbers are those numbers that have more than 2 factors. This means they can be divided by more than 2 numbers, excluding 1 and the number itself. 

Composite Numbers Examples 

You will get the composite number when you multiply the two least positive integers, including any divisor except 1. Composite numbers do not include 0 and 1. Moreover, the smallest composite number is  4. 

12 is divided by 1, 2, 3, 4, 6, and 12, and thus, it has more than 2 factors. Therefore, 12 is a composite number. More examples are 4, 6, 8, 9, and 10, as they can be divided by two integers. And the list may include any number that satisfies the condition for composite number. 

Kinds Of Composite Numbers

  1. Odd Composite Numbers 

Odd composite numbers include every number, which is an odd integer and is not prime numbers, such as 9, 15, 21, 25, 31, etc. 

  1. Even Composite Numbers 

The numbers that are neither an odd number nor a prime number are even composite. They include only the even non-prime numbers. Some examples are 4, 10, 16, 28, 56, and so on. 

Co-Prime Numbers

These numbers can be referred to as mutual primes or relative primes. Co-prime numbers are any two numbers that have only one factor. This means the number divided by only one number, 1, is called the co-prime number. 

Let’s see some of the examples of Co-Prime numbers.

If there are two numbers, 14 and 15, and you are asked to find out if these are the co-prime numbers or not, how will you do?

First, you must know the factors of the given number. 

The factor of 14 = 1, 2 and 7 

The factor of 15 = 1, 3 and 5

Now that you know the factors, you should search for the common factor in both numbers. Yes, the common factor is 1. Therefore, as per the rule and definition of the co-prime number, 14 and 15 are the co-prime numbers. 

You may be asked to find out the co-prime numbers, which may not have any common factor in them. The answer will be very simple that no number is the co-prime number.

Tricks To Find The Prime And Composite Number

It is not necessary to remember every prime and composite number. Once you know the trick, you will find it very easy to check whether the given number is prime or composite.

These are the tricks that you must know, which can help you differentiate between a prime and a composite number. 

  • If you can exactly divide the given number by any other number except 1, then the number is composite. 
  • As explained in the article, any even number greater than 2 is a composite number.
  • The number that is more than 2 and is the multiple of 2, then it is the non-prime number.
  • When there are 2 or more than 2 products of prime numbers in the prime factorisation, it is a composite number. 

Solved Examples

Question 1. Check whether  27 is a composite number or prime number.

Solution. Being an odd number, 27 need to be divided by the least odd prime number, which is 3. 

=  27/3 = 9

Again, we get 9, an odd number, so divide it by 3 one more time.

= 9/3 = 3

And again, we get odd numbers, 

= 3/3 = 1

Hence, 27 is divisible by 1, 3, 9 and 27 itself. Therefore, 27 is a composite number.

Question 2. What are the first ten composite numbers and prime numbers? 

Solution-  4, 6, 8, and 10 are the first ten Composite numbers, whereas 1, 3, 5, and 7 are the first ten Prime numbers. 

Question 3. Is zero a prime or composite number?

Solution. Zero is neither a prime nor a composite number. 

Things To Retain

Prime numbers are those numbers, which have only two factors: one is the number one and the number itself. In contrast, a composite number has more than two factors. There are also two types of composite numbers: odd composite numbers and even composite numbers. 

To find if a number is either prime or composite, you need to find out the prime factors. There is also a category of numbers called the co-prime numbers, which is a pair of numbers with only 1 as a common factor.

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