When \(N = 2^d \times a\) (\(a\): even), the set of the divisors of \(N\) is:

\(\left\{2 ^ i \times j \middle| 0 \leq i \leq d, j\text{ is a divisor of }a \right\}\)

Thus, if \(N\) has \(m\) odd divisors, it has \(dm\) even divisors.

Therefore, the answer is:

• Even, if \(N\) is divisible by \(4\);
• Same, if \(N\) is divisible by \(2\) but not by \(4\);
• Odd, if \(N\) is not divisible by \(2\).