There is a factory that makes widgets in different colors. The production time for each color is different. At the end of the day, all widgets produced that day are placed in boxes. On a certain day, the factory made 2,400 silver widgets and 4,950 green widgets. It takes 32 minutes to produce a bath of silver widgets and 22 minutes to produce a batch of green widgets. Determine the largest number of widgets that can be placed in each box if it is required that all boxes contain the same number of widgets and each box contains only one color. Explain the steps and problem-solving strategy used to determine the answer.

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