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There are two questions where I am having difficulty to solve. One of the question asks us the calculate the minimum number of square tiles required to cover a floor of dimension 247 ft x 209 ft. The particularly confusing part arises when we are not familiar with the intuition behind the calculation. Why would I really need to have square tiles to calculate a GCD is yet unknown to me here. Secondly, in another problem where we are required to find the number of wires of 22cm required to reach a length of 1m so that there is not wire that is left over also demands the usage of GCD. I am yet unfamiliar with how to solve these problems. Why GCD is being used particularly is unknown.

Black Panther
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    The side length $d$ of the tile must exactly divide both $247$ and $209$ for an exact fit. But $,d\mid a,b\iff d\mid \gcd(a,b)\ $ by the gcd universal property. Such tiling problems are one of the common geometrical motivations of the gcd. – Bill Dubuque Dec 12 '21 at 15:04
  • Yes but why is it the minimum number of tiles here? – Black Panther Dec 12 '21 at 15:18
  • @BillDubuque What about the next problem? Secondly, can you explain it more analytically that mathematics. Can you write a better answer? – Black Panther Dec 12 '21 at 15:23
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    If you decrease the tile size then you need more tiles. The second problem seems to be incorrectly stated. Please check it. It's not clear what you mean by "more analytically...". – Bill Dubuque Dec 12 '21 at 15:26

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