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2017 AMC 10BProblem 20P16-20~4 minPrint
Divisibility & FactorsPrimesBasic ProbabilitySet up the equation/formula and compute; no special trick needed

The number 21!=51,090,942,171,709,440,00021!=51,090,942,171,709,440,000 has over 60,00060,000 positive integer divisors. One of them is chosen at random. What is the probability that it is odd?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.