Prime and Composite Numbers


 
 
Concept Explanation
 

Prime and Composite Numbers

A prime number has only two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite. The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 since each of these numbers has only two factors,1 and itself.

When the area of a rectangle is a prime number, there is only one set of possible dimensions for that rectangle. When the area of a rectangle is a composite number, there are two or more sets of possible dimensions for that rectangle. Each set of dimensions is a pair of factors.

To determine if a number is prime or composite, follow these steps:

  • Find all factors of the number.
  • If the number has only two factors, 1 and itself, then it is prime.
  • If the number has more than two factors, then it is composite.
  • Illustration 1: Is the number 2 prime or composite?

    Solution: The factors of 2 are 1 , and 2. Hence,  2 is prime.

    Illustration 2: Is the number 9 prime or composite?

    Solution: The factors of 9 are 1 x 9, 3 x 3. Hence, 9 is composite.

    Illustration 3: Find the composite numbers which are multiple of 5 and less than 30.

    Solution: As multiples of 5 which are less than 30 are 5, 10, 15, 20, 25

    Now, factors of 5 = 1,5

      factors of 10 = 1, 2, 5, 10

      factors of  15 = 1, 3, 5, 15

      factors of 20 = 1, 2 , 4, 5 , 10, 20

      factors of  25 = 1, 5, 25

    As 10, 15,20, 25 has more than 2 factors, Hence all these numbers are composite.

    But 5 has only two factors, so 5 is prime.

    Hence, the composite numbers which are multiple of 5 and less than 30 are 10, 15, 20, 25

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Numbers which are not divisble by any other number except 1 and the number itself are called _____________

    Right Option : B
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    Explanation
    Question : 2

    _____ is the only even prime number.

    Right Option : C
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    Explanation
    Question : 3

    __________________ are 5 consecutive composite numbers less than 100 so that there is no prime number between them .

    Right Option : C
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    Explanation
     
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