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(f)   Divisibility by 4 and 8 is checked by adding the last 2 and 3 digits respectively and finding
                     if their sum is divisible by them or not.

                 (g)   A number is divisible by 11, if the difference between the sum of the digits at odd places
                     (from the right) and the sum of the digits at even places (from the right) is either 0 or
                     divisible by 11.
              7.  Properties of Divisibility
                 (a)  If a number is divisible by another number, it is also divisible by all its factors.
                 (b)  If a number is divisible by two co-prime numbers, it is also divisible by its product.

                 (c)   If two numbers are divisible by another number, then their sum or difference is also
                     divisible by that number.
              8.  Highest common factor (HCF) is the largest number that is a factor of the given numbers.
              9.  Lowest common multiple (LCM) is the smallest number that is a multiple of the given
                 numbers.

                                               Review Exercises


            Multiple ChoiCe Questions
              1.  Which of the following numbers is a perfect number?

                 (a)  2                  (b)  4                  (c)  6                  (d)  8
              2.  Which of the following numbers is divisible by 4?
                 (a)  25,13,784          (b)  18,20,741          (c)  70,12,345          (d)  68,54,321
              3.  What is the least value of * so that the number 9274*5 is divisible by 9?
                 (a)  0                  (b)  3                  (c)  4                  (d)  9
              4.  The number divisible by 11 is:
                 (a)  11,11,111          (b)  22,222             (c)  3,33,33,333        (d)  44,44,444
              5.  If 25*215 is divisible by 3, then * can take the value:
                 (a)  1                  (b)  3                  (c)  4                  (d)  5
              6.  Seive of Eratosthenes is a method to find:
                 (a)  perfect numbers  (b)  prime numbers        (c)  twin primes        (d)  co-primes

            solve Mentally

            True or False
              1.  A number divisible by 3 is also divisible by 6.
              2.  The numbers 8 and 9 are factors of 72.
              3.  Two consecutive prime numbers which are odd are called twin primes.
              4.  There is only one composite number between two primes.

              5.  Two numbers forming a twin prime are consecutive odd numbers.
              6.  There is only one composite number between twin primes.
              7.  Two co-prime numbers are always prime.
            Fill in the Blanks
              1.  A number is called ____________ if the sum of its factors, except itself, is greater than the
                 number.


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