How many even positive integers are there that are divisors of 720? How many even positive integers are there that are divisors of 720 ?
I know how to compute the number of divisors but how to compute the number of even or odd positive divisors of a number ?
If we list the divisors of 720 (using mathematica) : {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45,48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720} among these only 24 are even,I am looking for some tricks that can be used in solving similar kinds of problems during exam (under a minute solution).

An even number $2m$ is a factor of $720$ iff $m$ is a factor of $360$.
So it's the same problem as counting divisors of $360$. For
that it helps to consider the prime factorization of $360$.
