Prime 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 lesson, the details about prime numbers and composite numbers are given in detail along with examples and chart. The chart of composite and prime will help to identify them easily.

What are Prime and Composite Numbers?

A prime number is a number which has exactly two factors i.e. ‘1’ and number itself. 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. Apart from these two, there is also a similar category of number which are coprime numbers. The detailed explanation of these numbers is given below.

Prime Numbers

A prime number is the one which has exactly two factors, which means, it can be divided by only “1” and itself. But “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 ‘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?

The coprime-numbers or mutually primes or relatively primes are the two numbers which have only one common factor, which is 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

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.

Students can also practice by creating charts for prime and composite numbers from 1 to 1000.

Also Check: How to Find Prime Numbers?

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