In a school, the number of students in Grades 6, 7 and 8 was 184,276 and 322 , respectively. Students in each grade were divided into different sections, but every section across grades had the same number of students. For each section, a class teacher was appointed. What was the minimum number of class teachers required for the purpose?

Correct option is D

Given:

Number of students in Grade 6 = 184
Number of students in Grade 7 = 276
Number of students in Grade 8 = 322
Every section across grades had the same number of students.

Formula Used:

To find the minimum number of class teachers, we need to divide the total number of students in each grade by the number of students per section. The minimum number of class teachers required will be the greatest common divisor (GCD) of the total number of students across the three grades.

Solution:

Find the GCD of the number of students in the three grades (184, 276, and 322).
Using the Euclidean algorithm:
First, find the GCD of 184 and 276:
276 - 184 = 92
GCD(276, 184) = GCD(184, 92) = 92
Now, find the GCD of 92 and 322:
322 - 92 × 3 = 322 - 276 = 46
GCD(92, 322) = GCD(46, 92) = 46
So, the GCD of 184, 276, and 322 is 46.
The minimum number of students per section is 46. The number of sections for each grade is:
Grade 6: 184 ÷ 46 = 4
Grade 7: 276 ÷ 46 = 6
Grade 8: 322 ÷ 46 = 7
The total number of class teachers required is the sum of the sections in all grades:
4 + 6 + 7 = 17
The minimum number of class teachers required is 17.