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.