You are planning to lay square tiles on an entire 1352cm by 8788cm rectangular floor without cutting or overlapping any tiles. If all the tiles must be the same size, what is the least possible number of tiles you could use?

Question

whpalmer4 · Answer

Find the largest number that evenly divides both dimensions.

You can do this by factoring each number and multiplying the common factors

For example, if you had 8 and 12 as the dimensions:
8=2*2*2
12=2*2*3
They share  a pair of 2s as factors, so the largest square you could use would be one with a side length of 2*2=4

whpalmer4 · Answer

Having found the side length, the number of those tiles needed is the area of the floor divided by the area of 1 tile.

whpalmer4 · Answer

You can check your answer by dividing each dimension by the side length of the square to get the number of squares in each dimension.  Multiply the two and it should give you your answer.  In my example, 12/4=3 and 8/4=2, so 2*3=6 is the minimum possible number of tiles, just as we get from dividing the area of 8*12=96 by the tile area of 4*4=16 (96/16=6).