School books

At the beginning of the school year, the teacher distributed 480 workbooks and 220 textbooks. How many pupils could have the most in the classroom?

Result

n =  20

Solution:

$10 < n < 40 \ \\ \ \\ 480=2^5 \cdot 3 \cdot 5 \ \\ 220=2^2 \cdot 5 \cdot 11 \ \\ \text{GCD}(480, 220)=2^2 \cdot 5=20 \ \\ \ \\ n=GCD(480,220)=20 \ \\ \ \\ s=480/n=480/20=24 \ \\ u=220/n=220/20=11 \ \\ \ \\ n=20$

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