If r and s are positive integers, is \small \frac{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.

If statement(1) holds true, it is correct that is an integer.

If statement(2) holds true, it is not necessarily correct that is an integer.

Step-by-step explanation:

Given two positive integers and .

To check whether is an integer:

Condition (1):

Every factor of is also a factor of .

Let us consider an example:

which is an integer.

Actually, in this situation is a factor of .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that is an integer.

If statement(2) holds true, it is not necessarily correct that is an integer.

i dont know i just need points