Largest squares

How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?

Correct result:

n =  6

Solution:

a=16 dm b=96 dm  16=24 96=25⋅3 GCD(16,96)=24=16  c=GCD(a,b)=GCD(16,96)=16 dm  n=(a/c)⋅ (b/c)=(16/16)⋅ (96/16)=6a=16 \ \text{dm} \ \\ b=96 \ \text{dm} \ \\ \ \\ 16=2^4 \ \\ 96=2^5 \cdot 3 \ \\ \text{GCD}(16, 96)=2^4=16 \ \\ \ \\ c=GCD(a,b)=GCD(16,96)=16 \ \text{dm} \ \\ \ \\ n=(a/c) \cdot \ (b/c)=(16/16) \cdot \ (96/16)=6

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