A school has 336 boys and 252 girls. They are to stand in rows so that every row has the same number of students and each row has only boys or only girls. What is the least number of rows possible?

7Correct answerYour answer12Correct answerYour answer84Correct answerYour answer588Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Fewest rows means the most students per row: $\operatorname{HCF}(336, 252) = 84$ .
Rows of boys = $336 \div 84 = 4$ ; rows of girls = $252 \div 84 = 3$ .
Total rows = $4 + 3 = 7$ .

Worth noting

84 is the number of students in each row, not the number of rows; 12 multiplies the 4 boys' rows by the 3 girls' rows instead of adding. 588 is the total number of students.

Concept: HCF for equal rows
Typical timeTypical: 60 s
Your timeYours: —

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A school has 336 boys and 252 girls. They are to stand in rows so that every row has the same number of students and each row has only boys or only girls. What is the least number of rows possible?

Explanation