What is the largest number less than 2^64 which has exactly 90 positive divisors ?
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You can find the divisors of 90. Subtract 1 from each of them. And try to assign those divisors-1 as powers to some primes so that the multiplication of assigned divisors = 90. Take an assignment, and find the number as prime1^(divisor1-1) * prime2^(divisor2-1) * ... Take the maximum of those numbers which are less than 2^64.
Good luck!
If only there is another faster way.