Cool Factors - 1
Number Theory
Level
3
What is the smallest positive integer that has 9 factors ?????
The answer is 36.
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Such a number is of the form p^8 or p^2 q^2, where p, q are distinct primes. p^9 has factors 1, p, p^2, ..., p^8, and p^2 q^2 has factors p^a q^b, where a, b = 0, 1, or The minimal such numbers occur with p = 2 and q = 3, the smallest primes: 2^8 = 256 and 2^2 * 3^2 = 36.
36 is the smallest such positive integer.