How many of the positive divisors of 360 are even?

360 = $2^3\times 3^2\times 5$, so it has $(3+1)(2+1)(1+1)=24$ divisors in all. The odd divisors come from $3^2\times 5$ only: $(2+1)(1+1)=6$ of them. Even divisors = 24 − 6 = 18.