Many divides me
Number Theory
Level
4
Find the smallest positive integer such that the number of positive integral divisors of is 32.
The answer is 840.
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1 solution
Since 32 factors require a total of five distinct factors because their combinations taken 1 at a time, 2 at a time and so on will add up to 32 (2^5). Smallest of them are 2,3,4,5 and 7. I did not include 6 as it is covered by 2 and 3. Multiplying them will give 840.