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max of gcd of 3 products of elements of 3 disjoint partitions of {1,2,...,63}

Source: Czech-Polish-Slovak Junior Match 2014, Team p1 CPSJ

March 23, 2020
number theorygreatest common divisorSubsetsProduct

Problem Statement

The set of {1,2,3,...,63}\{1,2,3,...,63\} was divided into three non-empty disjoint sets A,BA,B. Let a,b,ca,b,c be the product of all numbers in each set A,B,CA,B,C respectively and finally we have determined the greatest common divisor of these three products. What was the biggest result we could get?
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