Prime and Composite Numbers


Prime and composite numbers are one of the basics of Mathematics. We are learning about these numbers since our primary classes. This is also a part of the number system or numeral system, where we learn about other types of numbers, such as even and odd numbers.  Here we will discuss about prime numbers, list of composite numbers, identification of both the numbers by drawing a chart from 1 to 100. Get to know about the co-prime numbers and how it is different from other prime ones.

The numbers which are exactly divisible by any other number apart from 1 and itself, are composite numbers and which cannot be divided exactly by a number apart from 1 and itself are prime numbers. To learn more about prime and composite numbers, read the complete article.

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: ‘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.

What are Coprime Numbers?

A co-prime or mutually prime or relatively prime 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.

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: ‘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

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 write the list of composite numbers from 1 to 100.

Prime and Composite Numbers Chart

  • Numbers which are in red colour are prime.
  • Numbers which are in black colour are composite.

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

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

Related Articles

If you want to get more details on the topic, download BYJU’S- The Learning App and see the interactive videos based upon the Number system.

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