Cattatackya

In the fictional, the rat-infested village of Cattatackya (where cats live) last month, each cat killed the same number of rats as every other cat. The total number of rat fatalities (deaths) during the month came to a total of 2117.
Less than 50 cats achieved this remarkable number of rat killings. How many cats were living in Cattatackya that month, and how many rats did each kill?

Answer
29 cats each killed 73 rats.

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