A rectangular piece of paper is 75 cm long and 60 cm wide. Now it is necessary to cut it into several identical squares, and the side length of the square is an integer centimeter, and no surplus is allowed. How many cutting methods are there? If the area of the square to be cut is the largest, how many pieces can be cut?
一张长方形的纸，长75厘米，宽60厘米．现在要把它裁成若干个相同的正方形，而且正方形边长为整数厘米，不允许有剩余，有几种裁法？如果要裁得的正方形面积最大，可以裁多少块？
<gadget id="calculator">15 * 15</gadget>
<output>225</output>

<gadget id="calculator">60 / 225</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">75 * (4/15)</gadget>
<output>20</output>

<result>20</result>