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 n^{3} 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 = 2^3*3 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 2*3=6. It can be larger but they are asking what must be the largest factor of n.

**If n is an integer and n ^{3} 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*.

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 n^{3} 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