Manhattan 5lb question - Factors

[Leaderboard]

See

Please help me understand this question

If n is an integer and n3 is divisible by 24, what is the largest number that must be a factor of n ? A)1 B)2 C)6 D)8 E)12 the correct option is C But I am not convinced if we take n=12 the 12x12x12 is divisible by 24 [the first part of the question] 12 is the largest factor 12 [ n=12 in this example ] that means E can also be the answer right?

Manhattan Chapter 13 question 28, page 451

Hi, Could someone please explain why the answer to the following question cannot be 12. I understand why it is 6 but the question asks for the largest factors of n which I believed could be 12. Q: If n is an integer and n3 is divisible by 24, what is the largest number that must be factor of n? a) 1 b) 2 c) 6 d) 8 e) 12 Answer: c

Manhattan 5lb question - Factors

Hey, For n^3 to be divisible by 24, n^3 should contain all the prime factors of 24. So now that we know that we need to prime factorize 24. 24 = 2^3 * 3 In any cube the number of prime factors are raised to a power of 3. For ex 8 = 2^3 , 64 = (2^2)^3 So we know that n should contain one 2 and a 3. Which means n has to be at least a 6. However, we don’t know if n^3 has more than 3 2s. It may or it may not. For n to be 12 we need 6 2s in n^3. Hence we cannot say for sure. The question is a “…

Also please format properly (for instance, either n³ or n^3).