Question

PLS HELLPP

Hector wants to tile his rectangle shed floor with rubber tiles. He found a company that will cut custom square tiles up to 60“ x 60“. The length of shed for is 240 inches and the width is 144 inches.


What is the side length of the largest square tile Hector can use to tile his shed floor so that they are no gaps or overlaps in the entire floor is covered

Answer 1

48 inches

Explanation:

The greatest common factor of 144 and 240 is 48. If Hector orders 48" square tiles, he can use 3 of them in the direction of the short dimension, and 5 of them in the direction of the long dimension.

The tiles can be 48 inches square.

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Using Euclid's algorithm to find the GCF, we have ...

240/144 = 1 r 96

144/96 = 1 r 48

96/48 = 2 r 0 . . . . . 48 is the GCF

At each step, if the remainder from the division is not zero, we replace the larger number with the remainder and do the division again. The divisor that gives a zero remainder is the GCF.