Primes, Divisibility

[gene.finley]

Hi,

So I noticed that I've been missing two types of problems
.

The first being problems that require us to determine if something is an integer or not. For example..

Is M/N an integer and then you get clues 1 and 2.

or

Is N/14 an integer?

I'm starting to realize although I understand prime factors and can tell you what they are I don't apply them when I should here. So I am looking for a rule or two to help me determine these things easy.

My question about the first two examples is, Does the N or 14 have to share prime factors with either the clues or M (for M/N) to be considered an integer? I can't tell if it needs to share or contain all of the prime factors which I think is a big difference.

[RonPurewal]

it would help immensely here if you could quote a specific problem or two. right now you've supplied a few fragments of problems, but that's not really a good enough basis for a meaningful response.

in general, though -- if you have trouble with theory on problems like these, you should consider plugging in specific numbers.
especially if it's a DS problem, this is often the key to making the problem easier to understand -- just throw in the first few specific cases that satisfy the statement(s), and then see whether a pattern emerges.