There are three iron wires, the lengths of which are 300 cm, 444 cm, and 516 cm respectively. Cut them into whole centimeter segments of the same length and as long as possible (no surplus is allowed), and fold each segment into a small square. Then these small squares are mixed together to form a rectangle (all these small squares must be used every time), how many possible rectangles are there?
有三根铁丝，分别长300厘米、444厘米、516厘米．把它们截成同样长且尽可能长的整厘米小段(不许剩余)，每小段折成一个小正方形．然后将这些小正方形混放在一起拼成一个长方形(每拼一次都必须用上所有这些小正方形)，这样可能拼成的长方形有多少种？
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