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21 September, 20:29

Find the smallest positive integer which have the same number of positive factors as 2015?

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  1. 21 September, 20:50
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    The prime factors of 2015 are:

    5 x 13 x 31

    We can choose to include or exclude each of these prime factors and that will form 2 x 2 x 2 = 8 factors, namely:

    1, 5, 13, 31, 65, 155, 403, 2015

    We want to form another number that has exactly 8 factors. So we need 3 primes with one that overlaps with 2015. The obvious choice is 2 x 3 x 5

    Answer:

    30 is the smallest positive number that also has 8 divisors (namely, 1, 2, 3, 5, 6, 10, 15, 30)
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