If N = 4P, where P is a prime number greater than 2, how many different…
2026
If N = 4P, where P is a prime number greater than 2, how many different positive even divisors does n have including n?
- A.
0
- B.
8
- C.
5
- D.
4
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Correct answer: D
Write N = 4P in prime-power form: N = 2^2 × P^1
Total number of divisors is (2+1)(1+1) = 3 × 2 = 6.
Number of odd divisors (set the power of 2 to 0) = (1+1) = 2.
Number of even divisors = total − odd = 6 − 2 = 4.
The even divisors are: 2, 4, 2P, and 4P (including N = 4P).