Page 40 - Maths Skill - 6
P. 40

38                                                                                                  Maths


        FACTORS
        Ranjeet has 8 chairs with him. He wants to arrange them in rows in
        such a way that each row has the same number of chairs. He arranges
        them in the following ways and matches the total number of chairs.

             (i)  1 chair in each row
                 Number of rows = 8
                 Total number of chairs = 1 × 8 = 8
            (ii)  2 chairs in each row

                 Number of rows = 4
                 Total number of chairs = 2 × 4 = 8
            (iii)  4 chairs in each row                            (iv)   8 chairs in each row
                 Number of rows = 2                                      Number of rows = 1

                 Total number of chairs = 4 × 2 = 8                      Total number of chairs = 8 × 1 = 8
                  From these calculations Ranjeet observes that 8 can be written as a product of two number in different
                ways.
                 8 = 1 × 8; 8 = 2 × 4; 8 = 4 × 2; 8 = 8 × 1
                  From 8 = 2 × 4, it can be said that 2 and 4 exactly divide 8. So, 2 and 4 are exact divisors of 8. From the
                other products 8 = 1 × 8, the exact divisors of 8 are found to be 1 and 8. Thus 1, 2, 4, and 8 are exact
                divisors of 8. They are called the factors of 8.
        A factor of a number is an exact divisor of that number. For example, 4 divides 20 exactly, therefore 4 is a factor
        of 20. Similarly, 3 divides 24 exactly, therefore 3 is a factor of 24.

        MULTIPLES

        A number is said to be a multiple of any of its factors.  For example, factors of 12 are 1, 2, 3, 4, 6 and 12.
        Thus, 12 is a multiple of each of these factors.
        If we multiply a number by natural numbers, i.e. 1, 2, 3, 4, ..., we get multiples of that number.

        PROPERTIES OF FACTORS AND MULTIPLES                                            Absorbing Facts

               ● The number 1 is a factor of every number.                          If ‘x’ is a factor of ‘y’ then ‘y’ is the
               ● Every number is a factor of itself.                                 multiple of ‘x’.
               ● Factor of a number is always less than or equal to the number itself.
               ● Every number is a multiple of 1 and itself.
               ● Every number is a multiple of each of its factors.
               ● Multiple of a number is always greater than or equal to the number itself.
               ● There is no largest multiple of a number.
               ● The number of multiples of a given number is infinite.

        TYPES OF NUMBERS

             (i)   Even Numbers: All multiples of 2 are called even numbers, i.e. 2, 4, 6, 8, 10, 12, 14, 16, .... are even
                                 numbers.
            (ii)   Odd Numbers: All other numbers which are not multiples of 2 are called odd numbers, i.e. 1, 3, 5, 7, 9,
                                 11, 13, 15, 17, ... are odd numbers.
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