Page 69 - Start Up Mathematics_6
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Be the 4-Juggly Jumper. You will land at 4 (write 4 below 4). Next you will land at 8 (write 4
             below 8). Continuing like this you will have 4 below 12, 16, 20 and 24. Fill the worksheet for
             5-Juggly Jumper, 6-Juggly Jumper and so on till 25-Juggly Jumper. Now answer the following
             questions.
             1.  Which number has only one jumper landing?
             2.  Which numbers have more than two jumpers landing?

             3.  How many Juggly Jumpers are landing on prime numbers?
             4.  Which number has the maximum Juggly Jumpers landing?
             5.  From the worksheet, find the HCF of:

                 (a) 12 and 18      (b) 9 and 19      (c) 8, 12 and 24


              Reason It Out!

              If n is an integer greater than 1 and divisible by some prime number p, such that p  ≤ n, then
                                                                                                   2
              n is composite. If there exists no such p then n is prime.
              Is 397 prime or composite?

              We have p = 2, 3, 5, 7, 11, 13, 17 and 19 (p  ≤ 397).
                                                           2
              Since no p divides 397. Hence, it is prime.
              Similarly check whether 1677 is prime or composite.


                                                    At a Glance

              1.  A factor of a number is an exact divisor of the number.

              2.  A multiple of a number is obtained by multiplying it by a natural number.
              3.  A number is said to be perfect, if the sum of all its factors is twice the number.
              4.  (a)  Any number which is divisible by 2 is called an even number.

                 (b)  Any number which is not divisible by 2 is called an odd number.
              5.  (a)   The numbers other than 1 whose only factors are 1 and the number itself are called prime
                     numbers.
                 (b)   Numbers having at least one factor other than 1 and the number itself are called composite
                     numbers.

                 (c)   If the difference between any two prime numbers is 2, then such a pair is called twin
                     prime.
              6.  Tests of Divisibility
                 (a)  A number is divisible by 10, if the digit at its ones place is 0.

                 (b)  A number is divisible by 5, if the digit at its ones place is either 0 or 5.
                 (c)  A number is divisible by 2, if the digit at its ones place is 0, 2, 4, 6 or 8.

                 (d)   A number is divisible by 3 and 9 respectively, if the sum of their digits is divisible by
                     3 and 9.
                 (e)  A number is divisible by 6, if it is divisible by both 2 and 3.


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