The number of students of Std 6th and Std 7th who went to visit the Tadoba Tiger Project at Chandrapur was 140 and 196 respectively. The students of each class are to be divided into groups of the same number of students. Each group can have a paid guide. What is the maximum number of students there can be in each group ? Why do you think each group should have the maximum possible number of students?

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Solution

Number of students of Std 6th = 140

Number of students of Std 7th = 196

The maximum same number of students of each class that can be divided into each group is the HCF of 140 and 196.

Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

Factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, 196

Common factors of 140 and 196: 1, 2, 4, 7, 14, 28

HCF of 140 and 196 = 28

∴ Maximum same number of students of each class that can be divided into each group = 28

Thus, the maximum number of students that can be in each group is 28.

Each group should have the maximum possible number of students so as to minimise the total amount paid to the guides.

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