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13 August, 23:40

What is the least whole number that has exactly 9 factors, including 1 and itself?

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  1. 14 August, 01:40
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    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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