Topic outline

    • Prime and Composite Numbers

      Prime Numbers

      Let’s observe the factors of few natural numbers.

      We can see that number 1 has only one factor (i.e. itself).There are numbers that have exactly two factors i.e.1 and the number itself. Such numbers are 2, 3, 5, etc. These numbers are prime numbers. A number is called prime when it can't be divided evenly by any number except 1 or itself.

      Therefore, Prime numbers are natural numbers that have only 2 factors i.e. 1 and itself.

      Example: 19

      19 have only two factors, 1 and 19. 19 cannot be divided evenly by numbers other than 1 or itself. So, 19 is a prime number.


      Co – Prime Numbers

      The two numbers are said to be co-prime numbers when there is no number, other than 1, that divides both the two given number evenly. The HCF of these numbers should be 1.

      Example: 6 and 35 are co-prime


      Composite Numbers

      Let’s observe factors of natural numbers again.

      There are numbers having more than two factors like 4, 6, etc. These numbers are composite numbers. When a number can be divided up evenly it is a Composite Number. A composite number has factors in addition to one and itself.

      Therefore, numbers having more than two factors are called Composite numbers.

      Example: 15

      15 have three factors, 1, 5 and 15. 15 can be divided evenly by numbers other than 1 or itself. So, 15 is a composite number.

      Prime and Composite Number Chart (1 to 100)

      1. 1 is neither a prime nor a composite number.

      2. All the numbers in orange box are prime numbers. All the numbers in white box, other than 1 are composite numbers.


      Important Notes:

      1. The numbers 0 and 1 are neither prime nor composite.

      2. Every prime number except 2 is odd.

      3. HCF of two prime numbers is always 1

      4. Even numbers are divisible by two and so all even numbers greater than two are composite numbers. Example: 2, 4, 6, 8, 10

      5. 1 is co-prime with every number.

      6. Every prime number is co-prime to each other. Example: 3 and 5

      7. Any two successive numbers are always co-primes.

      8. The sum two prime numbers can be even or odd.


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