Page 39 - Revised Maths Wisdom Class - 6

Prime Time 37

Thus, 12 is a multiple of each of these factors.

Properties of Factors
1. Every natural number can be divided exactly by 1, i.e., 1 is a factor of every number. For example,
8 ÷ 1 = 8; 3 ÷ 1 = 3, etc.

2. Every number is a factor of itself, i.e., every natural number can be divided exactly by itself. For example,
7 ÷ 7 = 1; 2 ÷ 2 = 1, etc.

3. Every factor of a number is an exact divisor of that number. For example, factors of 6 are 1, 2 and 3, i.e.,
6 ÷ 1 = 6; 6 ÷ 2 = 3 and 6 ÷ 3 = 2.

4. Every factor of a number is less than or equal to the number. For example, all the factors of 20 are 1, 2, 4, 5,
10 and 20. Each of these factors is either less than or equal to 20.
5. The number of factors of a given number are always limited. For example, 15 has factors as 1, 3, 5, and 15
i.e., it has 4 factors.
6. A number can be a factor of more than one number. For example, 7 is a factor of 7, 14, 21, 28, ....

Properties of Multiples

1. Every multiple of a number is greater than or equal to that number. For example, multiples of 7 are
7, 14, 21, 28, 35, ... etc. are either equal to or greater than 7.
2. Every number is a multiple of 1 and itself. For example, 8 × 1 = 8; So 8 is a multiple of 1 and itself.
3. The number of multiples of a given number is infinite. For example, multiples of 9 are 9, 18, 27, 36, 45, ....
and so on. These are infinite.
4. A number can be a multiple of several different numbers. For example, 18 is a multiple of 1, 2, 3, 6, 9
and 18.

Remember!er!
Rememb
› If 'x' is a factor of 'y' then 'y' is a multiple of 'x'.

ILLUSTRATIONS

Example 1: Find all the factors of 60. Example 2: Write the first five multiples of 13.
Solution: 60 = 1 × 60 Solution: 13 × 1 = 13
2 × 30 13 × 2 = 26

3 × 20 13 × 3 = 39
4 × 15 13 × 4 = 52
5 × 12 13 × 5 = 65

6 × 10
The factors of 60 are 1, 2, 3, 4, 5, 6, The first five multiples of 13 are 13,
10, 12, 15, 20, 30 and 60. 26, 39, 52 and 65.