An architectis desining a house in which a 104-square-foot room and a 130-square-foot room share a wall . what is the greatest possible integer length of the shared wall?

In my experience architects generally avoid number theory.

Let's called the shared wall .  The area is width times height, so the other walls are and .  We want the biggest s that gives integer quotients; that would be the greatest common factor of 104 and 130.





Greatest common factor and largest shared wall,



That's None of the Above, though 26x4 and 26x5 rooms are pretty goofy, probably why architects don't worry about number theory.

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