6

G.C.D is also referred to the Highest Common Factor (H.C.F) G -stands for greatest C- stands for common D- stands for divisor GCD refers to the largest common factor that can be divisible into a number without a remainder, or the highest common factor that can divide a number without a remainder. What is a factor? These are numbers we can multiply to get another number. For example 4 x 5 = 20. 4 and 5 are factors of 20 while 20 is the product. Therefore 4 and 5 are divisors of 20.

What are the divisors of 20?
Divisors of 20 are 1, 2, 4, 5, 10 and 20

• Note; that  1 x 20 = 20

• 2 x 10 = 20

• 4 x 5 = 20

• Therefore 1, 2, 4, 5, 10 and 20 are factors of 20

• Divisors are numbers that divide another number evenly without a remainder

Example 1

what is the GCD of 12,24 and 36

( i) list down the factors of each number.
( ii) list common factors in both numbers.
(iii) Identify the Highest/greatest common factor/divisor

Solution

12; 1,2,3,4,6,12

24; 1,2,3,4,6,8,12,24
36; 1,2,3,4,6,9,12,18,36

The common factors are; 1,2,3,4,6,12
The greatest common divisor is 12

Example 2 you can use division using least prime factor as below.

Wanyama wanted to share  his animal amongst his children.what is the greatest number of children who can share 60 cows and 42 goats?

Solution 

Wanyama wanted to share his animal amongst his children.what is the greatest number of children who can share 60 cows and 42 goats?

2 x 3 = 6; 6 is the greatest common divisor

Work out

1.What is the GCD of 16 and 36

2What is the of GCD 12,18and 24?

3.opiyo and onyango went fishing.opiyo caught 25 fish while onyango caught 35 fish .What is the greatest number of fish each could catch per hour, if they caught the same number of fish per hour.

4. What is the greatest common divisor of;

36,54,48

 5.What is the greatest number that can divide 42,66,102?

ANSWERS

• 4

• 12

• 5

• 6

• 6