In this question why do I assume that n=6, why can’t n=12?
is the answer c?
yes, and I get how to get to 6, I just don’t know why the answer isn’t 12 if they are asking for the largest
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 “must be” question not a “could be question”. If it were a “could be” question we could have assumed n to be 12.
Hope this helps 
Thanks!
Thank you!
No problem 
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
We have to assume that n^3 = 2^33 at a minimum because it is divisible by 24. So n must have 2 and 3 as it’s factors. So that has to be 23=6. It can be larger but they are asking what must be the largest factor of n.
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?
must, not can.
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If n is an integer and n is divisible by 24, what is the largest number that must be a factor of n?
Any explanation for this would be helpful!!
I suspect there is something missing with the formatting, otherwise the answer is trivially 24.
oh yes sorry the question is If n is an integer and n(cube)
is divisible by 24, what is the largest number that must be a factor of n?
See
Also please format properly (for instance, either n3 or n^3).
Thanks alot!!!
You said it can be larger. So 12 is larger than 6 and can be a factor of n. Since the question for the larget integer, 12 should be the correct answer right?
You’re right. Even I don’t get it, when I Googled it, the question was rephrased to “minimum”
No, what he is trying to say is 6 the largest factor among 1,2,3 and 6.
By using back solving, I came to know that the answer must be either 6 or 12.
After that, I just couldn’t solve it further, looked it up on greprepclub and also the 5lb answer key. But it doesn’t explain why the answer cannot be 12.
Thanks.
PS: Question from 5lb, Ch.13, Q28