GCF problem? "William is planning to create rectangular mosaic which measures 120..."

douglew

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GCF problem? "William is planning to create rectangular mosaic which measures 120..."

William is planningto create a rectangular mosaic which measures 120 cm by 144 cm. The mosaic will be covered completely with square pieces of colored glass. William has decided that he will purchase only one size of glass squares, and he does not plan to cut any of the pieces. If the art supply store only sells the glass squares in whole-number side lengths (measured in centimeters), find the smallest number of squares which William could use for his mosaic.

I thought this is a GCF problem and the GCF that I got from 120 and 144 is 24. However, the answer key says the answer is 30. Perhaps this is not a GCF problem? I do not understand why the answer is 30. Thanks for any help.
 
William is planningto create a rectangular mosaic which measures 120 cm by 144 cm. The mosaic will be covered completely with square pieces of colored glass. William has decided that he will purchase only one size of glass squares, and he does not plan to cut any of the pieces. If the art supply store only sells the glass squares in whole-number side lengths (measured in centimeters), find the smallest number of squares which William could use for his mosaic.

I thought this is a GCF problem and the GCF that I got from 120 and 144 is 24. However, the answer key says the answer is 30. Perhaps this is not a GCF problem? I do not understand why the answer is 30. Thanks for any help.

By taking the GCF of two sides of a rectangle - you have calculated each side of the largest square you need. However, you need to calculate the NUMBER of tiles needed.

So it IS a GCF problem - but you need to continue beyond that!

If you are using 24 cm X 24 cm tiles -

How many tiles would you need to cover the 120 cm side of the mosaic?

How many tiles would you need to cover the 144 cm side of the mosaic?

How many tiles would you need to cover the whole area of the mosaic?
 
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