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                     \ 09-Nov-2025  Bharat Arora   Proof-8                                    Reader’s Sign _______________________ Date __________

                    Multiples are thus the product of a number and the numbers 1, 2, 3, 4 and so on.

                     Multiples of 8                    Multiples of 10                     Multiples of 14

                         8 × 1 = 8                        10 × 1 = 10                         14 × 1 = 14

                        8 × 2 = 16                        10 × 2 = 20                         14 × 2 = 28
                        8 × 3 = 24         First 6        10 × 3 = 30          First 6        14 × 3 = 42         First 6
                                           multiples                           multiples                          multiples
                        8 × 4 = 32         of 8           10 × 4 = 40          of 10          14 × 4 = 56         of 14
                        8 × 5 = 40                        10 × 5 = 50                         14 × 5 = 70

                        8 × 6 = 48                        10 × 6 = 60                         14 × 6 = 84

                    The product of two or more numbers is called a multiple of each of these numbers.
                    For example, 16 × 5 = 80.

                    80 is the product of 16 and 5. So, 80 is a multiple of both 5 and 16.

                    properties of Multiples

                        1.  Every number is a multiple of 1.

                           For example, 1 × 2 = 2, 1 × 5 = 5, 1 × 7 = 7, 1 × 12 = 12, etc.

                      2.  The smallest (first) multiple of a number is the number itself.
                           For example, 5 × 1 = 5, 8 × 1 = 8, 11 × 1 = 11, etc.

                      3.  The multiple of a number is equal to or greater than the number.

                           For example, the multiples of 5 are 5, 10, 15, 20, 25, etc.

                      4.  There are infinite multiples of a number.

                           For example, multiples of 2 can be 2, 4, 6, 8, 10, 12, 14, 16, ...

                    Finding Multiples of a Number

                    example 1. Find the first three multiples of 4.
                    Solution. The multiples of a number can be found by

                    multiplying it by 1, 2, 3, 4 and so on.                                        To find the first three
                                                                                                  multiples of 4, multiply
                                     4 × 1 = 4    4 × 2 = 8    4 × 3 = 12                             4 by 1, 2 and 3.

                    Thus, the first three multiples of 4 are 4, 8, 12.

                    example 2. Find the 10th multiple of 13.
                                                                                                      To find the 10th
                    Solution. 13 × 10 = 130                                                       multiple of 13, multiply

                    Thus, the 10th multiple of 13 = 130.                                                 13 by 10.

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                                                                                           Multiples and Factors

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