Factors and multiples - 6

Highest Common Factor (HCF) / Greatest Common Divisor (GCD)

In the previous post, we discussed about finding factors of a given number. Let's take our discussion further and list factors of numbers 32 and 48. 

Factors of 32

32	=	1 x 32
	=	2 x 16
	=	4 x 8

Factors of 48

48	=	1 x 48
	=	2 x 24
	=	3 x 16
	=	4 x 12
	=	6 x 8

∴ Factors of 32: 1, 2, 4, 8, 16, 32

∴ Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

∴ Factors that are common between both 32 and 48: 1, 2, 4, 8, 16

Though there are 5 common factors between 32 and 48, the highest common factor is 16. Therefore, 16 is called as Highest Common Factor (HCF)/ Greatest Common Divisor (GCD) of the numbers 32 and 48.

But where do we apply our knowledge of HCF in our daily life?  

Suppose I have 2 pieces of cloth of length 90 cm and 144 cm each. I want to cut them into strips of equal and maximum possible lengths so that there is no extra cloth. What should be the length of each strip? 

Solution:
Find the HCF of 90 and 144

Step 1:
List the factors of 90 and 144
Factors of 90  : 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Step 2:
List factors common between factors of 90 and 144  
Common factors: 1, 2, 3, 6, 9, 18

Step 3:
Note the highest common factor (HCF)
∴ HCF of 90 and 144: 18

∴ Each cloth should be cut into strips of length 18 cm so that strips are of equal and maximum possible length. 

Can you think of more practical applications of HCF? Do let me know through comments.

Practice time:
Find the HCF

i	20, 45	v	42, 70
ii	16, 56	vi	24, 57
iii	25, 90	vii	60, 70
iv	48, 108	viii	81, 117

Answers