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                 \ 07-Nov-2024  Bharat Arora   Proof-8                                        Reader’s Sign _______________________ Date __________





                     (b)                                                3.
                                          12                                                        Divisible By
                          8      16                                   Number  Digit Total
                                      24   36    60                                    2   3  4   5  6   7  8  9  10  11
                         32    40     48                                27  2 + 7 = 9  No  Yes  No  No  No  No  No  Yes  No  No
                                      72
                          56          96    84                          74  7 + 4 = 11  Yes  No  No  No  No  No  No  No  No  No
                              64
                                 80          108                       132  1 + 3 + 2 = 6  Yes Yes Yes  No  Yes  No  No  No  No  Yes
                                                                       165  1 + 6 + 5 = 12  No  Yes  No  Yes  No  No  No  No  No  Yes
                           Multiples of 8  Multiples of 12
                                                                       184  1 + 8 + 4 = 13  Yes  No  Yes  No  No  No  Yes  No  No  No
                  12.  (7, 8) (Answers may vary)                       207  2 + 0 + 7 = 9  No  Yes  No  No  No  No  No  Yes  No  No
                Think and Answer
                  1.  2 (Even)   2.  4 (Even)                          280  2 + 8 + 0 = 10  Yes  No  Yes Yes  No  Yes Yes  No  Yes  No
                  3.  15; These are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.  131  1 + 3 + 1 = 5  No  No  No  No  No  No  No  No  No  No
                  4.  No, e.g., 6 has more number of factors than 9.   506  5 + 0 + 6 = 11  Yes  No  No  No  No  No  No  No  No  Yes
                Practice Time 5C                                       283  2 + 8 + 3 = 13  No  No  No  No  No  No  No  No  No  No
                  1.  (a)  F     (b)  T      (c)  T      (d)  F
                     (e)  F      (f)  T      (g)  F      (h)  F        147  1 + 4 + 7 = 12  No  Yes  No  No  No  Yes  No  No  No  No
                  2.  10; These are 53, 59, 61, 67, 71, 73, 79, 83, 89, 97  385  3 + 8 + 5 = 16  No  No  No  Yes  No  Yes  No  No  No  Yes
                  3.  (a)  Yes   (b)  Yes    (c)  No     (d)  Yes      250  2 + 5 + 0 = 7  Yes  No  No  Yes  No  No  No  No  Yes  No
                  4.  (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
                  5.  (3, 7), (3, 11), (3, 19) (Answers may vary)      477  4 + 7 + 7 = 18  No  Yes  No  No  No  No  No  Yes  No  No
                  6.  (a) Yes, 3 + 3 + 7 = 13, 5 + 7 + 11 = 23 (Answer may vary)  824  8 + 2 + 4 = 14  Yes  No  Yes  No  No  No  Yes  No  No  No
                     (b)  No.                                          753  7 + 5 + 3 = 15  No  Yes  No  No  No  No  No  No  No  No
                  7.  101, 103, 107, 109, 113, 127, 131, 137, 139,149,151,157, 163, 167, 173,
                     179, 181, 191, 193, 197, 199.                     1325  1 + 3 + 2 + 5 = 11 No  No  No  Yes  No  No  No  No  No  No
                  8.  One – 523                                         4.  (c)  46938
                Think and Answer                                        5.  (a)  Yes   (b)  No   (c)  No   (d)  Yes   (e)  Yes  (f)  No
                     210 = 2 × 3 × 5 × 7                                6.  (a)  Yes   (b)  No   (c)  Yes   (d)  Yes
                Practice Time 5D
                                                                        7.  (a)  48 = 5 + 43     (b)  64 = 11 + 53
                  1.  (a)    72              (b)   450                     (c)  96 = 7 + 89  [Answers may vary]
                                                                        8.  (a)  27 = 3 + 5 + 19   (b)  41 = 3 + 7 + 31
                           2    36              2     225                  (c)  63 = 3 + 7 + 53  [Answers may vary]
                                                                        9.  (a)  36 = 17 + 19    (b)  84 = 41 + 43
                             18    2               15     15
                                                                        10.  25 = 2 + 23; 26 = 3 + 23; 31 = 7 + 11 + 13    [Answers may vary]
                           9    2                3   5  3   5           11.

                        3    3

                     (c)   50                (d)      81
                        2    25                   9      9

                           5   5                3   3  3   3            12.  (a) – (iv)  (b) – (i)  (c) – (ii)  (d) – (iii)
                                                                        13.  (a)  Prime number         (b)  Composite number
                  2.  (a)  105 = 3 × 5 × 7   (b)  1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
                     (c)  1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2    (c)  Composite number        (d)  Composite number
                     (d)  729 = 3 × 3 × 3 × 3 × 3 × 3                   14.  175662       16. (a) 928389       (b)  819489
                  3.  (a)  3 × 47        (b)  2 × 2 × 2 × 5 × 5 × 5   Quick Check
                     (c)  11 × 11 × 11   (d)  5 × 5 × 5 × 5
                  4.  (a)  30 = 2 × 3 × 5   (b)  2310 = 2 × 3 × 5 × 7 × 11  1.  (a)  8   (b)  24   2.  (a) 1   (b)  2   (c)  1
                  5.  (a)  Yes   (b)  No   (c)  No   (d)  No          Think and Answer
                  6.  Perfect number: 496
                     Abundant number: 18                                   1152
                     Deficient number:11       [Answers may vary]     Quick Check
                  7.  (1184, 1210)         [Answers may vary]           1.  5              2.  150
                Think and Answer                                      Practice Time 5F
                     1324
                Think and Answer                                        1.  (a)  2   (b)  2   (c)  2
                     (3, 10) is a pair of co-prime                      2.  (a)  4   (b)  12   (c)  1   (d)  79
                Practice Time 5E                                        3.  (a)  84   (b)  90   (c)  336
                  1.  (a)  No   (b)  Yes   (c)  No   (d)  Yes           4.  (a)  240   (b)  180   (c)  12626
                  2.  (a)  No   (b)  No   (c)  Yes   (d)  Yes           5.  9:12 a.m.   6.  31 cm  7.  158   8.  1540   9.  12 minutes.

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