Prime and composite numbersare two of the types of number based on the number of factors they have.

What are Prime and Composite Numbers?

A prime number is a number whichhas exactly two factors i.e. it can be divided by only the number ‘1’ and itself. A composite numberhas more than two factors, which means apart from getting divided by number 1 and itself, it can also be divided by at least one integer or number. We don’t consider the number ‘1’ as a composite number. Apart from these two, there is also a similar category of number which are coprime numbers.

Prime Numbers

A prime number is the one which has exactly two factors, which means, it can be divided by only the number “1” and itself. But the number “1” is not a prime number.

Example of Prime Number:

3 is a prime number because 3 can be divided by only two number’s i.e. 1 and 3 itself.

3/1 = 3

3/3 = 1

In the same way, 2, 5, 7, 11, 13, 17 are prime numbers.

Composite Numbers

A composite number has more than two factors, which means apart from getting divided by number 1 and itself, it can also be divided by at least one integer or number. We don’t consider the number ‘1’ as a composite number.

Example of Composite Number:

12 is a composite number because it can be divided by 1,2,3,4,6 and 12. So, the number ‘12’ has 6 factors.

12/1 = 12

12/2 =6

12/3 =4

12/4 =3

12/6 =2

12/12 =1

What are Coprime Numbers?

Theco-primenumbersor mutually primes or relatively primes are the two numbers which have only one common factor, i.e. 1. Let us understand the concept with an example.

Suppose there are two numbers, 14 and 15. Find whether both are coprime or not.

The factors of 14 are 1, 2 and 7

The factors of 15 are 1, 3 and 5.

For both the numbers, we can see, the common factor is 1. Therefore 14 and 15 are coprime numbers. But if we consider another number say, 21, whose factors are 1, 3 and 7. Then, 21 is neither a coprime for 14 nor for 15.

Smallest Composite Number

As you have understood already about the composite number, now let us know the smallest number which is composite in nature. If we see the list of composite numbers, it starts from 4, 6, 8, 9, 10, 12, 14, 15, and so on. So you can see here 4 is the smallest number, which has factors apart from 1 and itself, such as;

Factors of 4 are 1, 2, and 4.

Prime and Composite Numbers List (Chart)

Identify the number of prime numbers given in the chart below and also with the help of this table, students can identify the list of composite numbers from 1 to 100.

Prime and Composite Numbers Chart

Note:

  • Numbers in “Red” are prime numbers
  • Numbers in “Black” are composite numbers

** From the given chart you can see the smallest prime number is 2 and the smallest composite number is 4.