# Question: 12 is a divisor of n

## Comment on 12 is a divisor of n

### The problem is the solutions

The problem is the solutions don't click on time. After i see the solution i am like, "Oh yea, that's true, not difficult". How to make things click the first time ? Please temme asap. Got the GRE tomorrow sir !

### Getting from "the solutions

Getting from "the solutions don't click on time" to "making things click the first time" is no easy feat, and it's not really something that happens over night (i.e., the day before the test).
I wish there were something I could say that could make that happen, but to be realistic, the phenomenon you're referring to is what happens when you take the time to fully master each topic.
Since your test is imminent, I suggest that you spend a little time developing the proper mindset, which I believe will do wonders for your score.
If you're interested, I wrote two articles on this topic:
- http://www.greenlighttestprep.com/articles/mindset-and-body-language-gre...
- http://www.greenlighttestprep.com/articles/junior-girls-volleyball-scori...

### Hi, I still don't quite

Hi, I still don't quite understand how you are able to conclude that g^h must be 2^3 based on the prime factorization. Able to explain again? Thanks.

### We can't say for sure whether

We can't say for sure whether g^h = 2^3 or g^h = 3^2.

What we do know is that one of the variables must be 2 and the other variable must be 3.

We know this because n is divisible by 12 AND that g and h are prime numbers. Since 12 = (2)(2)(3), then it must be the case that EITHER g = 2 and h = 3 OR g = 3 and h = 2

### Could you clear up a doubt of

Could you clear up a doubt of mine? I used 2 and 4 as 'G' and 'h' and got B and II only. Is the reason why that's wrong because 4 is not a prime factor of 12 and 3 is?

### Be careful. We're told that G

Be careful. We're told that G and H are prime.
So, we can't let H = 4 (as you have done)

### Yup, realized my mistake a

Yup, realized my mistake a few minutes after posting. Thank you.

### At 1:39, you've mentioned

At 1:39, you've mentioned that among 'g' and 'h', one of the numbers is 2 and the other is 3..I am not able to understand its reason.
Why can't one number be 4 and the other being 9?

And instead of using numbers, is there any other approach to solve this problem.

### The key here is that g and h

The key here is that g and h are PRIME numbers.
So, if n is divisible by 12 (aka 2x2x3), then g and h must be 2 and 3. But I do want to learn how to stock at some point