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CHAPTER-3: PLAYING WITH NUMBERS


               SUBTOPIC: Prime and Composite Numbers

               LESSON NOTES-2


                     Prime Numbers:The numbers other than 1 whose only factors are 1 and
                       the number itself are called prime number.
                       Ex- 5 = 1 x 5, 23 = 1 x 23
                     Composite Numbers: It is defined as a number having more than two
                       factors.
                       Ex- Factors of 9 are 1, 3 and 9. Therefore it is a composite number.
                       Note:
                       1 is neither prime nor composite number.
                       Any whole number greater than 1 is either a prime or composite number.


                     Even and odd numbers: An even number is a number that can be
                       divided into two equal groups. An odd number is a number that cannot be
                       divided into two equal groups.
                       Ex- 2, 4, 6, 8, 10, 12, 14 ... are even numbers and rest that is 1, 3, 5, 7, 9,
                       11... are odd numbers.
                       Note:2 is the smallest prime number which is even.
                       Every prime number except 2 is odd.

                     Twin primes: Twin primes are a pair of primes which differ by 2.
                       Ex- (3, 5); (5, 7); (11, 13); (17, 19); (29, 31); (41, 43)


                     Co-prime numbers: Any set of numbers which do not have any other
                       common factor other than 1 are called co-prime or relatively prime numbers.
                           Ex- Factors of 4 = 1, 2, 4
                              Factors of 15 = 1, 3, 15
                              This shows that 5 and 6 have no common factor other than 1. Therefore,
                           they are co-prime numbers.

                     Perfect Number: A perfect number is defined as a number for which sum
                       of all its factors is equal to twice the number.
                       Ex- 28, all the factors of 28 are 1, 2, 4, 7, 14 and 28. Adding these we have, 1
                       + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28. The sum of the factors of 28 is equal to
                       twice the number 28. Therefore 28 is a perfect number.
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