School year

At the beginning of the school year, 396 notebooks and 252 textbooks are ready to be distributed in the classroom. All pupils receive the same number of notebooks and the same amount of textbooks. How many pupils are there in the class if you know that there are more than 30 and less than 50?

Result

n =  36

Solution:

$396=2^2 \cdot 3^2 \cdot 11 \ \\ 252=2^2 \cdot 3^2 \cdot 7 \ \\ \text{GCD}(396, 252)=2^2 \cdot 3^2=36 \ \\ \ \\ n=GCD(396,252)=36 \ \\ s=396/n=396/36=11 \ \\ u=252/n=252/36=7 \ \\ \ \\ 30<n<50 \ \\ \ \\ n=36$

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