GMAT Number properties

[nandy1984]

If R and S are positive integers, is R/S an integer?

1) Every factor of S is also a factor of R.
2) Every Prime Factor of S is also a Prime factor of R.

My Approach:

Given: R & S posiitve integers....

Statement1: Every factor of S = Ever factor of R means both the numbers of same... (IS MY CONCLUSION CORRECT????)
SO SUFFICIENT....

Statement2: Every prime factor of S is also a Prime Factor of R...

Let S = 30 its prime factors are 5, 2,3...
Let R = 60 its prime factors are 5, 2, 2, 3.... so R/S is an integer... if S> R then the R/S will not be an integer...

So Answer is A.... Is my reasoning correct? Please explain if its wrong... Thanks...

[Anurag@Gurome]

(1) Every factor of S is also a factor of R implies when S will be reduced in R/S, we get an integer; SUFFICIENT.

(2) Every prime factor of S is also a prime factor of R. The powers of primes factors of S could be higher than powers of prime factors of R; NOT sufficient.

The correct answer is A.