Page 55 - Math Skill - 4

Factors and Multiples 53

™ Every number has a limited number of factors.
For example, all the factors of 16 are Fact-o-meter
� Every number is a factor of 0.
16 = 1 × 16 For example, 0 ÷ 13 = 0
Thus, 13 is a factor of 0.
16 = 2 × 8 0 ÷ 97 = 0 Thus, 97 is a factor of 0.

� As division by 0 is meaningless,
16 = 4 × 4 0 is not a factor of any number.

Thus, all the factors of 16 are 1, 2, 4, 8 and 16.

Common Factors
Consider the numbers 16 and 24.

Factors of 16 are 1, 2, 4, 8 and 16.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. 16 1 3, 6 24

Write the factors of 16 in the red circle and the factor 16 2
of 24 in the green circle. 4 12, 24

We will observe that 1, 2, 4 and 8 are in the common 8
part of the circles. Therefore, 1, 2, 4 and 8 are the
common factors of 16 and 24. Common factors of 16 and 24

Highest Common Factor or HCF
The Highest Common Factor or HCF is the largest factor common to the given numbers. Let

us learn to find out the common factor and the highest common factor (HCF) of two numbers
through examples.

Let’s Attempt

Example 1: Write all the common factors of:

(a) 8 and 18 (b) 12 and 20

Solution: (a) Factors of 8 are 1 , 2 , 4, 8.

Factors of 18 are 1 , 2 , 3, 6, 9, 18.

Thus, common factors of 8 and 18 are 1 and 2.

(b) Factors of 12 are 1 , 2 , 3, 4 , 6, 12

Factors of 20 are 1 , 2 , 4 , 5, 10, 20

Thus, common factors of 12 and 20 are 1, 2 and 4.