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3 February, 14:46

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

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  1. 3 February, 17:10
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    Four (2, 4, 2p, and 4p)

    Step-by-step explanation:

    Since p is a prime number greater than 2, then p=odd because the only prime number that is even is 2. Thus 4p = even at all times because 4 is even. Meaning that 4p has 4 even divisors: 2, 4, 2p, and 4p.

    Test cases:

    1. p = 3

    n = 4*3 = 12

    Divisors of 12 are 2, 4, 6 (2*3), 12 (4*3)

    2. p = 5

    n = 4*5 = 20

    Divisors of 20 are 2, 4, 10 (2*5), 20 (4*p)

    3. p = 17

    n = 4*17 = 68

    Divisors of 68 are 2, 4, 34 (2*17), 68 (4*17)
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