What is the greatest common factor of 24 and 36?

Factor both numbers: $24=2^3\cdot3$ and $36=2^2\cdot3^2$. The greatest common factor takes the smaller power of each shared prime: $2^2\cdot3=12$, choice C. Check: $24=12\cdot2$ and $36=12\cdot3$, and $2$ and $3$ share no further factor. Choice A ($6$) is a common factor, but not the greatest. Choice B ($8$) divides $24$ but not $36$. Choice D ($72$) is the least common multiple, which is the smallest number both divide into, not the largest number that divides both.