Mathematics

Question

the number n can be expressed as the product of four prime numbers, exactly three of which are the same. how many different positive divisors does n have, including n and 1 ?

1 Answer

  • Answer:

      8

    Step-by-step explanation:

    Give a prime factorization consisting of two primes, with one of them cubed, you want to know the number of positive integer divisors.

    Divisors

    The number of divisors is the product of the exponents of the prime factorization, each increased by 1.

    Application

    Your number is ...

      n = (a^3)(b^1)

    so the number of positive divisors is ...

      (3+1)(1+1) = 4·2 = 8

    The number n has 8 different positive divisors.

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    Additional comment

    The divisors are ...

      1, a, b, a², ab, a³, a²b, a³b

    Example: 24 = 2³·3 has divisors ...

      1, 2, 3, 4, 6, 8, 12, 24

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