I can not figure out the answer to this problem. Can someone help please ?

Is the answer C.6 ?? prime factoring 24 gives 2^3*3. so n^3 must be 2^3*3^3 which 216 so n must 6. largest number the must be a factor of n is n itself so the answer is 6.

If the answer is wrong, please let me know

Yeah, sounds correct!

@hbksanjeev Thank you for your response. I understand that 24 is 2^3 x 3^1 , but I do not get the following in your answer.

n^3 must be 2^3* 3^3 which 216

n^3 which can also be written as n*n*n is divisible by 24. if we break down 24 then we get 2*2*2*3. If we make pair then one n (from n*n*n) must be divisible by 2*3. That means the highest factor of n is 2*3 = 6.