shuyinchen2015 shuyinchen2015
  • 27-02-2018
  • Mathematics
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What is the least whole number that has exactly 9 factors, including 1 and itself?

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mathmate
mathmate mathmate
  • 28-02-2018
If the whole number has exactly 9 (odd number) factors, it will have to be a perfect square.
All squares of primes have exactly three factors.
So start with perfect squares (skipping perfect squares of primes)
4^2=16 {1,2,4,8,16}  5 factors.
6^2=36 {1,2,3,4,6,9,12,18,36}  9 factors.

Answer: 36 is the least whole number that has exactly 9 factors.
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