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In a class there are 48 boys and 60 girls. The class teacher wants to divide the students into smaller groups such that each group contains the same number of students and each group contains only boys or only girls. What is the minimum possible number of group that can be created ?
Given :
Number of boys is $48$.
Number of girls is $60$.
The class is divided into groups such that, the same number of students in each group, and each group contains only boys or girls.
To find :
We have to find the minimum possible number of groups.
Solution :
Each group contains only boys or girls. So, we need to find HCF of $48$ and $60$.
$Factors of 48 = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 48$.
$Factors of 60 = 1 , 2 , 3 , 5 , 6 , 10 , 12 , 20 , 30 , 60$.
The Highest Common Factor of $48$ and $60$ is $12$.
So, the number of students each group $= 12$.
Total number of students $= 48 + 60 = 108 $
$Number of groups = \frac{Total number of students }{Number of students each group}$
$Number of groups = \frac{108 }{12}$
$Number of groups = 9$
Therefore, Minimum possible groups is 9.
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