Question

How many factors of $720$ are divisible by $4$ but not by $16$?

Answer 1

Estimate the number of factors:

Factors of $720$ are

$1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360$ and$720$.

Out of these,

$4,8,12,16,20,24,36,40,48,60,72,80,120,144,180,240,360$ and $720$ are divisible by$4$.

The number of factors divisible by$4=18$.

Out of these, $4,8,12,20,24,36,40,60,72,120,180,360$ are not divisible$16$.

Hence, the number of factors divisible by $4$ but not divisible by $16$ is$12$.