document.write( "Question 604355: A rectangular floor that measures 78 inches by 102 inches
\n" ); document.write( "is to be completely covered with square tiles. The tiles are
\n" ); document.write( "available in sizes with only whole-number side lengths. What
\n" ); document.write( "is the smallest number of uncut tiles that could be used to
\n" ); document.write( "cover the floor? \n" ); document.write( "

Algebra.Com's Answer #381207 by KMST(5328) $\"\"$ $\"About$

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The width of the floor can be covered by 1-inch wide tiles, using 78 tiles.
\n" ); document.write( "We can use 2-inch wide tiles, using 39 of them, because (2 inch) x 39 = 78 inch.
\n" ); document.write( "We could also use 3-inch wide tiles (26 of them) because 3 x 26 = 78.
\n" ); document.write( "We could even use 6-inch wide tiles (13 of them) because 6 x 13= 78.
\n" ); document.write( "In fact we could cover the width of the floor with tiles of any number of inches in width, as long as that number is a factor of 78 inches. Even 13, or 26, or 39 inches would work.
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\n" ); document.write( "However, we want the width of the tiles (in inches) to also be a factor of 102, the length of the room in inches
\n" ); document.write( "102 is divisible by 1, 2, 3, and 6 (102 = 6 x 17), but it is not evenly divided by 13, 26, or 39.
\n" ); document.write( "The greatest common factor of 78 and 102 is 6.
\n" ); document.write( "With 6 inch by 6 inch tiles, we would fit 17 tiles along the 102 inch length of the room and 13 tiles along the 78 inch width.
\n" ); document.write( "So we would have 13 rows of 17 tiles (or 17 rows of 13 tiles, depending on how you look at it).
\n" ); document.write( "In any case, we would have 13 times 17 tiles, for a total of 221 tiles, with the least number of the biggest square tiles we can get.
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