There are 32 girls and 40 boys in a class. If they have to stand in equal rows such that each row will only be occupied by either girls or boys, what is the greatest number of students that could be in each row?

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Solution

The correct option is C 8
To solve this problem, first we have to break down both the numbers into prime factors.

The prime factorization of 32 is: 2 × 2 × 2 × 2 × 2
The prime factorization of 40 is: 2 × 2 × 2 × 5

Thus, the greatest common factor of 32 and 40 is 8.

Hence, the students must be arranged in rows of 8.

Additionally,
Number of rows occupied by girls: 32 ÷ 8 = 4
Number of rows occupied by boys: 40 ÷ 8 = 5

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