each player is given a rectangular piece of graph paper that is 56cm long and 84 cm wide. The horizontal and vertical lines are spaced 1 cm apart. The paper is to be cut along the grid (graph) lines into square pieces that are all the same size without having any paper left over. The winner is the one who cuts the largest square pieces of paper. What would be the length in centimeters of the side of each winning square.

Question

each player is given a rectangular piece of graph paper that is 56cm long and 84 cm wide.  The horizontal and vertical lines are spaced 1 cm apart.  The paper is to be cut along the grid (graph) lines into square pieces that are all the same size without having any paper left over.  The winner is the one who cuts the largest square pieces of paper. What would be the length in centimeters of the side of each winning square.

Reiny · Accepted Answer

let each side of the largest square be x cm
so along the long side we can fit 84/x squares and along the short side we can fit 56/x squares

56 = 7*4*2 = 28*2
84 = 7*4*3 = 28*3

since 28 is the largest whole number that divides into both 56 and 84, the largest square is
28 x 28 cm.
(there will be 6 of these)

check: 6(28x28) = 4704
56x84 = 4704