A teacher wants to arrange 2,800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

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Solution

The correct option is B
52

$Number of students who participated in the arrangement = 2, 800 - 96 = 2, 704$

$On prime factorizing 2,704, we get,$

$\begin{matrix} 2 & 2, 704 2 & 1, 352 2 & 676 2 & 338 13 & 169 13 & 13 1 \end{matrix}$

$2, 704 = 2 \times 2 \times 2 \times 2 \times 13 \times 13$

$\sqrt{2, 704} = 2 \times 2 \times 13 = 52$

$Hence, the required number of rows = 52$

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A teacher wants to arrange 2,800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

The correct option is B 52 Number of students who participated in the arrangement =2,800−96=2,704 On prime factorizing 2,704, we get, 22,70421,352267623381316913131 2,704=2× 2× 2× 2× 13× 13 √2,704=2× 2× 13=52 Hence, the required number of rows =52